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Physics Subject Area Test MECHANICS: DYNAMICS Dynamics: Newton’s Laws of Motion Newton’s First Law Force Dynamics – connection between force and motion Force – any kind of push or pull required to cause a change in motion (acceleration) measured in Newtons (N) Dynamics: Newton’s Laws of Motion Newton’s First Law of Motion Newton’s First Law of Motion First Law – Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it. First Law – (Common) An object at rest remains at rest, and a object in motion, remains in motion unless acted upon by an outside force. Newton’s First Law of Motion Newton’s Laws are only valid in an Inertial Frame of Reference For example, if your frame of reference is an accelerating car – a cup in that car will slide with no apparent force being applied Newton’s First Law of Motion An inertial frame of reference is one where if the first law is valid Inertia – resistance to change in motion * Dynamics: Newton’s Laws of Motion Mass * Mass Mass – a measurement of inertia A larger mass requires more force to accelerate it Weight – is a force, the force of gravity on a specific mass * Dynamics: Newton’s Laws of Motion Newton’s Second Law Newton’s Second Law Second Law – acceleration is directly proportional to the net force acting on it, and inversely proportional to its mass. -the direction is in the direction of the net force Easier to see as an equation more commonly written a F m F ma * Newton’s Second Law F – the vector sum of the forces In one dimension this is simply adding or subtracting forces. Free Body Diagram The most important step in solving problems involving Newton’s Laws is to draw the free body diagram Be sure to include only the forces acting on the object of interest Include any field forces acting on the object Do not assume the normal force equals the weight F table on book F Earth on book Objects in Equilibrium Objects that are either at rest or moving with constant velocity are said to be in equilibrium Acceleration of an object can be modeled as zero: a 0 Mathematically, the net force acting on the object is zero F 0 Equivalent to the set of component equations given by F x 0 F y 0 A lamp is suspended from a chain of negligible mass The forces acting on the lamp are the downward force of gravity the upward tension in the chain Applying equilibrium gives F y 0 T Fg 0 T Fg A traffic light weighing 100 N hangs from a vertical cable tied to two other cables that are fastened to a support. The upper cables make angles of 37 ° and 53° with the horizontal. Find the tension in each of the three cables. Conceptualize the traffic light Assume cables don’t break Nothing is moving Categorize as an equilibrium problem No movement, so acceleration is zero Model as an object in equilibrium F x 0 F y 0 Need 2 free-body diagrams Apply equilibrium equation to light T3 F g 100 N Apply equilibrium equations to knot F F y 0 T3 F g 0 x Fy T1x T2 x T1 cos 37 T2 cos 53 0 T1y T2 y T3 y T1 sin 37 T2 sin 53 100 N 0 cos 37 T2 T1 1.33 T1 cos 53 T1 60 N T2 1.33 T1 80 N F y 0 T3 F g 0 T3 F g 100 N Suppose a block with a mass of 2.50 kg is resting on a ramp. If the coefficient of static friction between the block and ramp is 0.350, what maximum angle can the ramp make with the horizontal before the block starts to slip down? F F Newton 2nd law: x mg sin s N 0 y N mg cos 0 Then F So y N mg cos mg sin s mg cos 0 tan s 0 . 350 tan 1 ( 0 . 350 ) 19 . 3 A block of mass m1 on a rough, horizontal surface is connected to a ball of mass m2 by a lightweight cord over a lightweight, frictionless pulley as shown in figure. A force of magnitude F at an angle θ with the horizontal is applied to the block as shown and the block slides to the right. The coefficient of kinetic friction between the block and surface is μk. Find the magnitude of acceleration of the two objects. We all remember the fun see-saw of our youth. But what happens if . . . Moral Both the masses and their positions affect whether or not the “see saw” balances. * M1 M2 d1 Need: M1 d1 = M2 d2 d2 The great Greek mathematician Archimedes said, “give me a place to stand and I will move the Earth,” meaning that if he had a lever long enough he could lift the Earth by his own effort. * We can think of leaving the masses in place and moving the fulcrum. It would have to be a pretty long see-saw in order to balance the school bus and the race car, though! M1 M2 d1 d2 (We still) need: M1 d1 = M2 d2