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Physics Semester I Final Review ConcepTest 3.2a Vector Components I 1) it doubles If each component of a vector is doubled, what happens to the angle of that vector? 2) it increases, but by less than double 3) it does not change 4) it is reduced by half 5) it decreases, but not as much as half ConcepTest 3.2a Vector Components I 1) it doubles If each component of a vector is doubled, what happens to the angle of that vector? 2) it increases, but by less than double 3) it does not change 4) it is reduced by half 5) it decreases, but not as much as half The magnitude of the vector clearly doubles if each of its components is doubled. But the angle of the vector is given by tan q = 2y/2x, which is the same as tan q = y/x (the original angle). Follow-up: If you double one component and not the other, how would the angle change? ConcepTest 3.4a A small cart is rolling at constant velocity on a flat track. It fires a ball straight up into the air as it moves. After it is fired, what happens to the ball? Firing Balls I 1) it depends on how fast the cart is moving 2) it falls behind the cart 3) it falls in front of the cart 4) it falls right back into the cart 5) it remains at rest ConcepTest 3.4a A small cart is rolling at constant velocity on a flat track. It fires a ball straight up into the air as it moves. After it is fired, what happens to the ball? In the frame of reference of the cart, the ball only has a vertical component of velocity. So it goes up and comes back down. To a ground observer, both the cart and the ball have the same horizontal velocity, so the ball still returns into the cart. Firing Balls I 1) it depends on how fast the cart is moving 2) it falls behind the cart 3) it falls in front of the cart 4) it falls right back into the cart 5) it remains at rest when viewed from train when viewed from ground ConcepTest 3.4b Now the cart is being pulled along a horizontal track by an external force (a weight hanging over the table edge) and accelerating. It fires a ball straight out of the cannon as it moves. After it is fired, what happens to the ball? Firing Balls II 1) it depends upon how much the track is tilted 2) it falls behind the cart 3) it falls in front of the cart 4) it falls right back into the cart 5) it remains at rest ConcepTest 3.4b Now the cart is being pulled along a horizontal track by an external force (a weight hanging over the table edge) and accelerating. It fires a ball straight out of the cannon as it moves. After it is fired, what happens to the ball? Firing Balls II 1) it depends upon how much the track is tilted 2) it falls behind the cart 3) it falls in front of the cart 4) it falls right back into the cart 5) it remains at rest Now the acceleration of the cart is completely unrelated to the ball. In fact, the ball does not have any horizontal acceleration at all (just like the first question), so it will lag behind the accelerating cart once it is shot out of the cannon. ConcepTest 3.4c The same small cart is now rolling down an inclined track and accelerating. It fires a ball straight out of the cannon as it moves. After it is fired, what happens to the ball? Firing Balls III 1) it depends upon how much the track is tilted 2) it falls behind the cart 3) it falls in front of the cart 4) it falls right back into the cart 5) it remains at rest ConcepTest 3.4c The same small cart is now rolling down an inclined track and accelerating. It fires a ball straight out of the cannon as it moves. After it is fired, what happens to the ball? Firing Balls III 1) it depends upon how much the track is tilted 2) it falls behind the cart 3) it falls in front of the cart 4) it falls right back into the cart 5) it remains at rest Because the track is inclined, the cart accelerates. However, the ball has the same component of acceleration along the track as the cart does! This is essentially the component of g acting parallel to the inclined track. So the ball is effectively accelerating down the incline, just as the cart is, and it falls back into the cart. ConcepTest 3.5 You drop a package from a plane flying at constant speed in a straight line. Dropping a Package 1) quickly lag behind the plane while falling 2) remain vertically under the plane while falling Without air resistance, 3) move ahead of the plane while falling the package will: 4) not fall at all ConcepTest 3.5 You drop a package from a plane flying at constant speed in a straight line. Dropping a Package 1) quickly lag behind the plane while falling 2) remain vertically under the plane while falling Without air resistance, 3) move ahead of the plane while falling the package will: 4) not fall at all Both the plane and the package have the same horizontal velocity at the moment of release. They will maintain this velocity in the x-direction, so they stay aligned. Follow-up: What would happen if air resistance were present? ConcepTest 3.6a From the same height (and at the same time), one ball is dropped and another ball is fired horizontally. Which one will hit the ground first? Dropping the Ball I 1) the “dropped” ball 2) the “fired” ball 3) they both hit at the same time 4) it depends on how hard the ball was fired 5) it depends on the initial height ConcepTest 3.6a From the same height (and at the same time), one ball is dropped and another ball is fired horizontally. Which one will hit the ground first? Dropping the Ball I 1) the “dropped” ball 2) the “fired” ball 3) they both hit at the same time 4) it depends on how hard the ball was fired 5) it depends on the initial height Both of the balls are falling vertically under the influence of gravity. They both fall from the same height. Therefore, they will hit the ground at the same time. The fact that one is moving horizontally is irrelevant – remember that the x and y motions are completely independent !! Follow-up: Is that also true if there is air resistance? ConcepTest 3.6b In the previous Dropping the Ball II 1) the “dropped” ball 2) the “fired” ball problem, which ball has the greater velocity at ground level? 3) neither – they both have the same velocity on impact 4) it depends on how hard the ball was thrown ConcepTest 3.6b In the previous problem, which ball has the greater velocity at ground level? Dropping the Ball II 1) the “dropped” ball 2) the “fired” ball 3) neither – they both have the same velocity on impact 4) it depends on how hard the ball was thrown Both balls have the same vertical velocity when they hit the ground (since they are both acted on by gravity for the same time). However, the “fired” ball also has a horizontal velocity. When you add the two components vectorially, the “fired” ball has a larger net velocity when it hits the ground. Follow-up: What would you have to do to have them both reach the same final velocity at ground level? ConcepTest 3.6c A projectile is launched from the ground at an angle of 30o. At what point in its trajectory does this projectile have the least speed? Dropping the Ball III 1) just after it is launched 2) at the highest point in its flight 3) just before it hits the ground 4) halfway between the ground and the highest point 5) speed is always constant ConcepTest 3.6c A projectile is launched from the ground at an angle of 30o. At what point in its trajectory does this projectile have the least speed? The speed is smallest at the highest point of its flight path because the ycomponent of the velocity is zero. Dropping the Ball III 1) just after it is launched 2) at the highest point in its flight 3) just before it hits the ground 4) halfway between the ground and the highest point 5) speed is always constant ConcepTest 4.1a Newton’s First Law I A book is lying at 1) there is a net force but the book has too much inertia rest on a table. 2) there are no forces acting on it at all The book will 3) it does move, but too slowly to be seen remain there at 4) there is no net force on the book rest because: 5) there is a net force, but the book is too heavy to move ConcepTest 4.1a Newton’s First Law I A book is lying at 1) there is a net force but the book has too much inertia rest on a table. 2) there are no forces acting on it at all The book will 3) it does move, but too slowly to be seen remain there at 4) there is no net force on the book rest because: 5) there is a net force, but the book is too heavy to move There are forces acting on the book, but the only forces acting are in the y-direction. Gravity acts downward, but the table exerts an upward force that is equally strong, so the two forces cancel, leaving no net force. ConcepTest 4.1b Newton’s First Law II A hockey puck slides on ice at constant velocity. What is the net force acting on the puck? 1) more than its weight 2) equal to its weight 3) less than its weight but more than zero 4) depends on the speed of the puck 5) zero ConcepTest 4.1b Newton’s First Law II A hockey puck slides on ice at constant velocity. What is the net force acting on the puck? 1) more than its weight 2) equal to its weight 3) less than its weight but more than zero 4) depends on the speed of the puck 5) zero The puck is moving at a constant velocity, and therefore it is not accelerating. Thus, there must be no net force acting on the puck. Follow-up: Are there any forces acting on the puck? What are they? ConcepTest 4.7a Gravity and Weight I What can you say about the 1) Fg is greater on the feather 2) Fg is greater on the stone 3) Fg is zero on both due to vacuum 4) Fg is equal on both always force of gravity Fg acting on a stone and a feather? 5) Fg is zero on both always ConcepTest 4.7a Gravity and Weight I What can you say 1) Fg is greater on the feather 2) Fg is greater on the stone about the force of 3) Fg is zero on both due to vacuum gravity Fg acting 4) Fg is equal on both always 5) Fg is zero on both always on a stone and a feather? The force of gravity (weight) depends on the mass of the object!! The stone has more mass, therefore more weight. ConcepTest 4.7b Gravity and Weight II What can you say about the 1) it is greater on the feather 2) it is greater on the stone 3) it is zero on both due to vacuum 4) it is equal on both always acceleration of gravity acting on the stone and the feather? 5) it is zero on both always ConcepTest 4.7b Gravity and Weight II What can you say 1) it is greater on the feather about the acceleration 2) it is greater on the stone of gravity acting on the stone and the 3) it is zero on both due to vacuum 4) it is equal on both always 5) it is zero on both always feather? The acceleration is given by F/m so here the mass divides out. Since we know that the force of gravity (weight) is mg, then we end up with acceleration g for both objects. Follow-up: Which one hits the bottom first? ConcepTest 4.9a Going Up I A block of mass m rests on the floor of 1) N > mg an elevator that is moving upward at 2) N = mg constant speed. What is the relationship between the force due to 3) N < mg (but not zero) gravity and the normal force on the 4) N = 0 block? 5) depends on the size of the elevator v m ConcepTest 4.9a Going Up I A block of mass m rests on the floor of 1) N > mg an elevator that is moving upward at 2) N = mg constant speed. What is the relationship between the force due to 3) N < mg (but not zero) gravity and the normal force on the 4) N = 0 block? 5) depends on the size of the elevator The block is moving at constant speed, so it must have no net force on it. The forces v on it are N (up) and mg (down), so N = mg, just like the block at rest on a table. m ConcepTest 4.9b Going Up II A block of mass m rests 1) N > mg on the floor of an 2) N = mg elevator that is accelerating upward. What is the relationship 3) N < mg (but not zero) 4) N = 0 5) depends on the size of the elevator between the force due to gravity and the normal a force on the block? m ConcepTest 4.9b Going Up II A block of mass m rests on the 1) N > mg floor of an elevator that is 2) N = mg accelerating upward. What is 3) N < mg (but not zero) the relationship between the 4) N = 0 force due to gravity and the 5) depends on the size of the elevator normal force on the block? The block is accelerating upward, so it must have a net upward force. The N m a>0 forces on it are N (up) and mg (down), so N must be greater than mg in order to give the net upward force! Follow-up: What is the normal force if the elevator is in free fall downward? mg S F = N – mg = ma > 0 \ N > mg ConcepTest 4.10 Normal Force Below you see two cases: a physics student pulling or pushing a sled with a force F which is applied at an angle q. In which case is the normal force greater? 1) case 1 2) case 2 3) it’s the same for both 4) depends on the magnitude of the force F 5) depends on the ice surface Case 1 Case 2 ConcepTest 4.10 Normal Force Below you see two cases: a physics student pulling or pushing a sled with a force F which is applied at an angle q. In which case is the normal force greater? 1) case 1 2) case 2 3) it’s the same for both 4) depends on the magnitude of the force F 5) depends on the ice surface Case 1 In Case 1, the force F is pushing down (in addition to mg), so the normal force needs to be larger. In Case 2, the force F is pulling up, against gravity, so the normal force is lessened. Case 2 ConcepTest 4.11 On an Incline Consider two identical blocks, 1) case A one resting on a flat surface 2) case B and the other resting on an incline. For which case is the normal force greater? 3) both the same (N = mg) 4) both the same (0 < N < mg) 5) both the same (N = 0) ConcepTest 4.11 On an Incline Consider two identical blocks, 1) case A one resting on a flat surface 2) case B and the other resting on an incline. For which case is the normal force greater? 3) both the same (N = mg) 4) both the same (0 < N < mg) 5) both the same (N = 0) In Case A, we know that N = W. y In Case B, due to the angle of the incline, N < W. In fact, we N f can see that N = W cos(q). q q W Wy x ConcepTest 4.12 Climbing the Rope When you climb up a rope, the first thing you do is pull down on the rope. How do you manage to go up the rope by doing that?? 1) this slows your initial velocity, which is already upward 2) you don’t go up, you’re too heavy 3) you’re not really pulling down – it just seems that way 4) the rope actually pulls you up 5) you are pulling the ceiling down ConcepTest 4.12 Climbing the Rope When you climb up a rope, the first thing you do is pull down on the rope. How do you manage to go up the 1) this slows your initial velocity, which is already upward 2) you don’t go up, you’re too heavy 3) you’re not really pulling down – it just seems that way 4) the rope actually pulls you up 5) you are pulling the ceiling down rope by doing that?? When you pull down on the rope, the rope pulls up on you!! It is actually this upward force by the rope that makes you move up! This is the “reaction” force (by the rope on you) to the force that you exerted on the rope. And voilá, this is Newton’s Third Law. ConcepTest 4.14a Collision Course I 1) the car A small car 2) the truck collides with a 3) both the same 4) it depends on the velocity of each large truck. Which experiences the greater impact force? 5) it depends on the mass of each ConcepTest 4.14a Collision Course I A small car collides 1) the car with a large truck. 2) the truck Which experiences the greater impact 3) both the same 4) it depends on the velocity of each 5) it depends on the mass of each force? According to Newton’s Third Law, both vehicles experience the same magnitude of force. ConcepTest 4.14b Collision Course II 1) the car In the collision 2) the truck between the 3) both the same car and the truck, which has the greater acceleration? 4) it depends on the velocity of each 5) it depends on the mass of each ConcepTest 4.14b Collision Course II In the collision between the car and 1) the car 2) the truck 3) both the same the truck, which has 4) it depends on the velocity of each the greater 5) it depends on the mass of each acceleration? We have seen that both vehicles experience the same magnitude of force. But the acceleration is given by F/m so the car has the larger acceleration, since it has the smaller mass. ConcepTest 4.21 Going Sledding Your little sister 1) pushing her from behind wants you to give 2) pulling her from the front her a ride on her sled. On level 3) both are equivalent 4) it is impossible to move the sled 5) tell her to get out and walk ground, what is the easiest way to accomplish this? 1 2 ConcepTest 4.21 Going Sledding Your little sister wants you to give her a ride on her sled. On level ground, what is the easiest way to accomplish this? 1) pushing her from behind 2) pulling her from the front 3) both are equivalent 4) it is impossible to move the sled 5) tell her to get out and walk In Case 1, the force F is pushing down (in addition to mg), so the normal force is larger. In Case 2, the force F 1 is pulling up, against gravity, so the normal force is lessened. Recall that the frictional force is proportional to the normal force. 2 ConcepTest 4.22 Will it Budge? A box of weight 100 N is at rest on a floor where ms = 0.5. A rope is attached to the box and pulled horizontally with tension T = 30 N. Which way does the box move? 1) moves to the left 2) moves to the right 3) moves up 4) moves down 5) the box does not move Static friction (ms = 0.4 ) m T ConcepTest 4.22 Will it Budge? A box of weight 100 N is at rest on a floor where ms = 0.5. A rope is attached to the box and pulled horizontally with tension T = 30 N. Which way does the box move? 1) moves to the left 2) moves to the right 3) moves up 4) moves down 5) the box does not move The static friction force has a maximum of msN = 40 N. The tension in the rope is only 30 N. Static friction (ms = 0.4 ) m T So the pulling force is not big enough to overcome friction. Follow-up: What happens if the tension is 35 N? What about 45 N? ConcepTest 4.23a Sliding Down I A box sits on a flat board. You lift one end of the board, making an angle with the floor. As you increase the angle, the box will eventually begin to slide down. Why? 1) component of the gravity force parallel to the plane increased 2) coeff. of static friction decreased 3) normal force exerted by the board decreased 4) both #1 and #3 5) all of #1, #2 and #3 Normal Net Force Weight ConcepTest 4.23a Sliding Down I A box sits on a flat board. You lift one end of the board, making an angle with the floor. As you increase the angle, the box will eventually begin to slide down. Why? 1) component of the gravity force parallel to the plane increased 2) coeff. of static friction decreased 3) normal force exerted by the board decreased 4) both #1 and #3 5) all of #1, #2 and #3 As the angle increases, the component of weight parallel to the plane increases and the component perpendicular to the Normal plane decreases (and so does the normal force). Since friction depends on normal Net Force force, we see that the friction force gets smaller and the force pulling the box down the plane gets bigger. Weight ConcepTest 5.1 To Work or Not to Work Is it possible to do work on an 1) yes object that remains at rest? 2) no ConcepTest 5.1 To Work or Not to Work Is it possible to do work on an 1) yes object that remains at rest? 2) no Work requires that a force acts over a distance. If an object does not move at all, there is no displacement, and therefore no work done. ConcepTest 5.2a Friction and Work I A box is being 1) friction does no work at all pulled across a 2) friction does negative work rough floor at a 3) friction does positive work constant speed. What can you say about the work done by friction? ConcepTest 5.2a Friction and Work I A box is being pulled across a rough floor at a 1) friction does no work at all constant speed. What 2) friction does negative work can you say about the 3) friction does positive work work done by friction? Friction acts in the opposite N displacement direction to the displacement, so the work is negative. Or using the Pull f definition of work (W = F d cos q ), since q = 180o, then W < 0. mg ConcepTest 5.2b Friction and Work II Can friction ever do positive work? 1) yes 2) no ConcepTest 5.2b Friction and Work II Can friction ever do positive work? 1) yes 2) no Consider the case of a box on the back of a pickup truck. If the box moves along with the truck, then it is actually the force of friction that is making the box move. ConcepTest 5.2c Play Ball! In a baseball game, the catcher stops a 90-mph 1) catcher has done positive work pitch. What can you say 2) catcher has done negative work about the work done by 3) catcher has done zero work the catcher on the ball? ConcepTest 5.2c Play Ball! In a baseball game, the catcher stops a 90-mph 1) catcher has done positive work pitch. What can you say 2) catcher has done negative work about the work done by 3) catcher has done zero work the catcher on the ball? The force exerted by the catcher is opposite in direction to the displacement of the ball, so the work is negative. Or using the definition of work (W = F d cos q ), since q = 180o, then W < 0. Note that because the work done on the ball is negative, its speed decreases. Follow-up: What about the work done by the ball on the catcher? ConcepTest 5.2d Tension and Work A ball tied to a 1) tension does no work at all string is being 2) tension does negative work whirled around in 3) tension does positive work a circle. What can you say about the work done by tension? ConcepTest 5.2d Tension and Work A ball tied to a string is being whirled around in 1) tension does no work at all a circle. What can you 2) tension does negative work say about the work done 3) tension does positive work by tension? No work is done because the force acts in a perpendicular direction to the displacement. Or using the definition of work (W = F d cos q ), since q = 180o, then W < 0. T v Follow-up: Is there a force in the direction of the velocity? ConcepTest 5.3 Force and Work 1) one force A box is being pulled 2) two forces up a rough incline by a 3) three forces rope connected to a 4) four forces pulley. How many 5) no forces are doing work forces are doing work on the box? ConcepTest 5.3 Force and Work A box is being pulled up a 1) one force rough incline by a rope 2) two forces connected to a pulley. 3) three forces How many forces are 4) four forces doing work on the box? 5) no forces are doing work Any force not perpendicular to the motion will do work: N does no work N T T does positive work f f does negative work mg does negative work mg ConcepTest 5.8a Slowing Down If a car traveling 60 1) 20 m km/hr can brake to a 2) 30 m stop within 20 m, what is its stopping distance if it is traveling 120 km/hr? Assume that the braking force is the same in both cases. 3) 40 m 4) 60 m 5) 80 m ConcepTest 5.8a Slowing Down If a car traveling 60 km/hr can brake to a stop within 20 m, what is its stopping distance if 1) 20 m 2) 30 m 3) 40 m it is traveling 120 km/hr? 4) 60 m Assume that the braking force 5) 80 m is the same in both cases. F d = Wnet = DKE = 0 – 1/2 mv2 thus: |F| d = 1/2 mv2 Therefore, if the speed doubles, the stopping distance gets four times larger. ConcepTest 5.13 Up the Hill Two paths lead to the top of a big hill. One is steep and direct, while the other is twice as long but less steep. How much more potential energy would you gain if you take the longer path? 1) the same 2) twice as much 3) four times as much 4) half as much 5) you gain no PE in either case ConcepTest 5.13 Up the Hill Two paths lead to the top of a big hill. One is steep and direct, while the other is twice as long but less steep. How much more potential energy would you gain if you take the longer path? 1) the same 2) twice as much 3) four times as much 4) half as much 5) you gain no PE in either case Since your vertical position (height) changes by the same amount in each case, the gain in potential energy is the same. Follow-up: How much more work do you do in taking the steeper path? Follow-up: Which path would you rather take? Why? ConcepTest 5.16 Down the Hill Three balls of equal mass start from rest and roll down different ramps. All ramps have the same height. Which ball has the greater speed at the bottom of its ramp? 1 2 3 4) same speed for all balls ConcepTest 5.16 Down the Hill Three balls of equal mass start from rest and roll down different ramps. All ramps have the same height. Which ball has the greater speed at the bottom of its ramp? 4) same speed for all balls 1 2 3 All of the balls have the same initial gravitational PE, since they are all at the same height (PE = mgh). Thus, when they get to the bottom, they all have the same final KE, and hence the same speed (KE = 1/2 mv2). Follow-up: Which ball takes longer to get down the ramp? ConcepTest 5.18a Water Slide I Paul and Kathleen start from rest at 1) Paul the same time on frictionless water 2) Kathleen slides with different shapes. At the 3) both the same bottom, whose velocity is greater? Conservation of Energy: Ei = mgH = Ef = 1/2 mv2 therefore: gH = 1/2 v2 Since they both start from the same height, they have the same velocity at the bottom. ConcepTest 5.18b Water Slide II Paul and Kathleen start from rest at the same time on frictionless water slides with different shapes. Who makes it to the bottom first? 1) Paul 2) Kathleen 3) both the same ConcepTest 5.18b Water Slide II Paul and Kathleen start from 1) Paul rest at the same time on 2) Kathleen frictionless water slides with 3) both the same different shapes. Who makes it to the bottom first? Even though they both have the same final velocity, Kathleen is at a lower height than Paul for most of her ride. Thus she always has a larger velocity during her ride and therefore arrives earlier! ConcepTest 5.21a Time for Work I Mike applied 10 N of 1) Mike force over 3 m in 10 2) Joe 3) both did the same work seconds. Joe applied the same force over the same distance in 1 minute. Who did more work? ConcepTest 5.21a Time for Work I Mike applied 10 N 1) Mike of force over 3 m 2) Joe in 10 seconds. 3) both did the same work Joe applied the same force over the same Both exerted the same force over the same distance in 1 displacement. Therefore, both did the same minute. Who did amount of work. Time does not matter for more work? determining the work done. ConcepTest 5.21b Time for Work II Mike performed 5 J of work in 1) Mike produced more power 10 secs. Joe did 3 J of work 2) Joe produced more power in 5 secs. Who produced the 3) both produced the same greater power? amount of power ConcepTest 5.21b Time for Work II Mike performed 5 J of work in 1) Mike produced more power 10 secs. Joe did 3 J of work 2) Joe produced more power in 5 secs. Who produced the 3) both produced the same greater power? amount of power Since power = work / time, we see that Mike produced 0.5 W and Joe produced 0.6 W of power. Thus, even though Mike did more work, he required twice the time to do the work, and therefore his power output was lower. ConcepTest 5.22b Energy Consumption Which contributes 1) hair dryer more to the cost of 2) microwave oven your electric bill each 3) both contribute equally month, a 1500-Watt 4) depends upon what you cook in the oven hair dryer or a 600- 5) depends upon how long each one is on Watt microwave 600 W oven? 1500 W ConcepTest 5.22b Energy Consumption 1) hair dryer Which contributes more to 2) microwave oven the cost of your electric bill 3) both contribute equally each month, a 1500-Watt 4) depends upon what you cook in the oven hair dryer or a 600-Watt 5) depends upon how long each one is on microwave oven? We already saw that what you actually pay for 600 W is energy. To find the energy consumption of an appliance, you must know more than just the power rating—you have to know how long it was running. 1500 W ConcepTest 6.3a Momentum and Force A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s momentum compare to the rate of change of the pebble’s momentum? 1) greater than 2) less than 3) equal to ConcepTest 6.3a Momentum and Force A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s momentum compare to the rate of change of the pebble’s momentum? 1) greater than 2) less than 3) equal to The rate of change of momentum is, in fact, the force. Remember that F = Dp/Dt. Since the force exerted on the boulder and the pebble is the same, then the rate of change of momentum is the same. ConcepTest 6.3b Velocity and Force A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s velocity compare to the rate of change of the pebble’s velocity? 1) greater than 2) less than 3) equal to ConcepTest 6.3b Velocity and Force A net force of 200 N acts on a 100 kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s velocity compare to the rate of change of the pebble’s velocity? 1) greater than 2) less than 3) equal to The rate of change of velocity is the acceleration. Remember that a = Dv/Dt. The acceleration is related to the force by Newton’s 2nd Law (F = ma), so the acceleration of the boulder is less than that of the pebble (for the same applied force) because the boulder is much more massive. ConcepTest 6.4 Collision Course 1) the car A small car and a 2) the truck large truck collide 3) they both have the same momentum change head-on and stick 4) can’t tell without knowing the final velocities together. Which one has the larger momentum change? ConcepTest 6.4 Collision Course A small car and a large 1) the car truck collide head-on 2) the truck and stick together. 3) they both have the same momentum change Which one has the larger momentum change? 4) can’t tell without knowing the final velocities Since the total momentum of the system is conserved, that means that Dp = 0 for the car and truck combined. Therefore, Dpcar must be equal and opposite to that of the truck (–Dptruck) in order for the total momentum change to be zero. Note that this conclusion also follows from Newton’s 3rd Law. Follow-up: Which one feels the larger acceleration? ConcepTest 6.6 Watch Out! You drive around a curve in a narrow one-way street at 30 mph when you see an identical car heading straight toward you at 30 mph. You have two options: hit the car head-on or swerve into a massive concrete wall (also headon). What should you do? 1) hit the other car 2) hit the wall 3) makes no difference 4) call your physics teacher! 5) get insurance! ConcepTest 6.6 Watch Out! You drive around a curve in a narrow 1) hit the other car one-way street at 30 mph when you see 2) hit the wall an identical car heading straight toward 3) makes no difference you at 30 mph. You have two options: 4) call your physics teacher! hit the car head-on or swerve into a massive concrete wall (also head-on). 5) get insurance! What should you do? In both cases your momentum will decrease to zero in the collision. Given that the time Dt of the collision is the same, then the force exerted on YOU will be the same!! If a truck is approaching at 30 mph, then you’d be better off hitting the wall in that case. On the other hand, if it’s only a mosquito, well, you’d be better off running him down... ConcepTest 6.7 Impulse A small beanbag and a bouncy rubber ball are dropped from the same height above the floor. They both have the same mass. Which one will impart the greater impulse to the floor when it hits? 1) the beanbag 2) the rubber ball 3) both the same ConcepTest 6.7 Impulse A small beanbag and a bouncy rubber ball are dropped from the same height above the floor. They both have the same mass. Which one will impart the greater 1) the beanbag 2) the rubber ball 3) both the same impulse to the floor when it hits? Both objects reach the same speed at the floor. However, while the beanbag comes to rest on the floor, the ball bounces back up with nearly the same speed as it hit. Thus, the change in momentum for the ball is greater, because of the rebound. The impulse delivered by the ball is twice that of the beanbag. For the beanbag: For the rubber ball: Dp = pf – pi = 0 – (–mv ) = mv Dp = pf – pi = mv – (–mv ) = 2mv Follow-up: Which one imparts the larger force to the floor? ConcepTest 6.9a Going Bowling I A bowling ball and a ping-pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, which takes a longer time to bring to rest? 1) the bowling ball 2) same time for both 3) the ping-pong ball 4) impossible to say p p ConcepTest 6.9a Going Bowling I A bowling ball and a ping-pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, which takes a longer time to bring to rest? We know: Dp Fav = Dt 1) the bowling ball 2) same time for both 3) the ping-pong ball 4) impossible to say so Dp = Fav Dt p Here, F and Dp are the same for both balls! It will take the same amount of time to stop them. p ConcepTest 6.9ba Going Bowling II A bowling ball and ping-pong ball are rolling toward you with the same 1) the bowling ball 2) same distance for both 3) the ping-pong ball 4) impossible to say momentum. If you exert the same force to stop each one, for p which is the stopping distance greater? p ConcepTest 6.9b Going Bowling II A bowling ball and a ping-pong ball are rolling toward you with 1) the bowling ball 2) same distance for both the same momentum. If you exert 3) the ping-pong ball the same force to stop each one, 4) impossible to say for which is the stopping distance greater? Use the work-energy theorem: W = DKE. The ball with less mass has the greater speed (why?), and thus the greater KE (why again?). In order to remove that KE, work must be done, where W = Fd. Since the force is the same in both cases, the distance needed to stop the less massive ball must be bigger. p p ConcepTest 6.10a Elastic Collisions I Consider two elastic collisions: 1) 1) a golf ball with speed v hits a 2) stationary bowling ball head-on. 3) 2) a bowling ball with speed v hits a stationary golf ball head-on. In which case does the golf ball have the greater speed after the collision? situation 1 situation 2 both the same at rest v at rest 1 v 2 ConcepTest 6.10a Elastic Collisions I Consider two elastic collisions: 1) a golf ball with speed v hits a stationary bowling ball head-on. 2) a bowling ball with speed v hits a stationary golf ball head-on. In which case does the golf ball have the greater speed after the collision? Remember that the magnitude of the relative velocity has to be equal before and after the collision! 1) situation 1 2) situation 2 3) both the same v 1 In case 1 the bowling ball will almost remain at rest, and the golf ball will bounce back with speed close to v. In case 2 the bowling ball will keep going with speed close to v, hence the golf ball will rebound with speed close to 2v. 2v v 2 ConcepTest 6.10b Elastic Collisions II Carefully place a small rubber ball (mass m) on top of a much bigger basketball (mass M) and drop these from some height h. What is the velocity of the smaller ball after the basketball hits the ground, reverses direction and then collides with small rubber ball? 1) zero 2) v 3) 2v 4) 3v 5) 4v ConcepTest 6.10b Elastic Collisions II Carefully place a small rubber ball (mass m) on top of a much bigger basketball (mass M) and drop these from some height h. What is 1) zero the velocity of the smaller ball after the basketball hits the ground, reverses direction and then collides with small rubber ball? 4) 3v 2) v 3) 2v 5) 4v • Remember that relative 3v m velocity has to be equal v v before and after collision! Before the collision, the v v M basketball bounces up v with v and the rubber ball is coming down with v, (a) (b) (c) so their relative velocity is –2v. After the collision, it Follow-up: With initial drop height h, how therefore has to be +2v!! high does the small rubber ball bounce up? ConcepTest 6.14b Recoil Speed II A cannon sits on a 1) 0 m/s stationary railroad 2) 0.5 m/s to the right flatcar with a total mass of 1000 kg. When a 10-kg cannon ball is fired to the left at a speed of 50 m/s, what is the recoil speed of the flatcar? 3) 1 m/s to the right 4) 20 m/s to the right 5) 50 m/s to the right ConcepTest 6.14b Recoil Speed II A cannon sits on a stationary railroad flatcar with a total mass of 1000 kg. When a 10-kg cannon ball is fired to the left at a speed of 50 m/s, what is the recoil speed of the flatcar? Since the initial momentum of the system was zero, the final total momentum must also be zero. Thus, the final momenta of the cannon ball and the flatcar must be equal and opposite. pcannonball = (10 kg)(50 m/s) = 500 kg-m/s pflatcar = 500 kg-m/s = (1000 kg)(0.5 m/s) 1) 0 m/s 2) 0.5 m/s to the right 3) 1 m/s to the right 4) 20 m/s to the right 5) 50 m/s to the right ConcepTest 6.15 Gun Control When a bullet is fired from a gun, the bullet and the gun have equal and opposite momenta. If this is true, then why is the bullet deadly? (whereas it is safe to hold the gun while it is fired) 1) it is much sharper than the gun 2) it is smaller and can penetrate your body 3) it has more kinetic energy than the gun 4) it goes a longer distance and gains speed 5) it has more momentum than the gun ConcepTest 6.15 Gun Control When a bullet is fired from a gun, the bullet and the gun have equal and opposite momenta. If this is true, then why is the bullet deadly? (whereas it is safe to hold the gun while it is fired) 1) it is much sharper than the gun 2) it is smaller and can penetrate your body 3) it has more kinetic energy than the gun 4) it goes a longer distance and gains speed 5) it has more momentum than the gun While it is true that the magnitudes of the momenta of the gun and the bullet are equal, the bullet is less massive and so it has a much higher velocity. Since KE is related to v2, the bullet has considerably more KE and therefore can do more damage on impact. ConcepTest 6.16a Crash Cars I If all three collisions below are totally inelastic, which one(s) will bring the car on the left to a complete halt? 1) I 2) II 3) I and II 4) II and III 5) all three ConcepTest 6.16a Crash Cars I If all three collisions below 1) I are totally inelastic, which 2) II one(s) will bring the car on the left to a complete halt? In case I, the solid wall clearly stops the car. In cases II and III, since ptot = 0 before the collision, then ptot must also be zero after the collision, which means that the car comes to a halt in all three cases. 3) I and II 4) II and III 5) all three ConcepTest 6.16b Crash Cars II 1) I If all three collisions below are totally inelastic, which terms of lost energy)? 3) III 4) II and III 5) all three one(s) will cause the most damage 2) II (in ConcepTest 6.16b Crash Cars II If all three collisions below are totally inelastic, which one(s) 1) I 2) II 3) III will cause the most damage 4) II and III (in terms of lost energy)? 5) all three The car on the left loses the same KE in all 3 cases, but in case III, the car on the right loses the most KE because KE = 1/2 m v2 and the car in case III has the largest velocity. ConcepTest 6.17 Shut the Door! You are lying in bed and 1) the superball you want to shut your 2) the blob of clay bedroom door. You have a 3) it doesn’t matter -- they will be equally effective superball and a blob of clay (both with the same mass) sitting next to you. Which one would be more effective to throw at your door to close it? 4) you are just too lazy to throw anything ConcepTest 6.17 Shut the Door! You are lying in bed and you want to 1) the superball shut your bedroom door. You have a 2) the blob of clay superball and a blob of clay (both 3) it doesn’t matter -- they with the same mass) sitting next to you. Which one would be more effective to throw at your door to will be equally effective 4) you are just too lazy to throw anything close it? The superball bounces off the door with almost no loss of speed, so its Dp (and that of the door) is 2mv. The clay sticks to the door and continues to move along with it, so its Dp is less than that of the superball, and therefore it imparts less Dp to the door.