Force and Newton Laws Aqeel Mohamed &Christian Martinez Dynamics • Observation of objects in nature • If a body is not under the influence of force, it is at rest or a natural state. - Aristotle • Claim is refuted by Newtonian Law Motion • Change in the location of an object over a period of time. • Speed and direction is maintained of an object is in motion. • Newton’s Three Laws help in our understanding of the properties of motion. Newton’s First Law: Inertia • Matter would resist a change in motion. • If a force acts upon an object, it would continue to move indefinitely in the direction the force acted in. • The larger a mass, the more inertia (resistance to change in motion) an object would have. Newton’s Second Law:Acceleration • An unbalanced force acting on an object causes the object to accelerate in the direction of the force. • Acceleration is the change in magnitude of velocity or direction. • Situation occurs when resultant force or the net force is NOT zero. Formula • Acceleration is directly proportional to the net force. • Acceleration is indirectly proportional to an object’s mass • a= F/m • Where “a” is acceleration, “F” the net force, and “m” the mass of the object Force • Expressed in Newtons (N) • 1(N)= 1kg x m/s^2 • Net force can be represented as the product of an object’s mass and accelaration • F=ma • Force is directly proportional to acceleration Third Law of Motion • For every reaction, there is an equal and opposite reaction. • Forces always occur in pairs when acting on an object. Second object of two objects will exert a force equal to the force the first object originally exerted. • Never act on the same object or could be combined. (same magnitude but opposite in direction) Law of Universal Gravitation • All objects have the ability to attract other objects. • Gravitational pull is proportional to mass. The greater the mass, the greater the gravitational pull. Weight • The “pull” felt by objects on Earth • Product of acceleration due to gravity and an object’s mass. • Weight is a “force due to gravity” • F= ma g=a • F=mg • g= 9.81 m/s^2 (acceleration due to gravity Gravitational Force of Two Objects • Gravitational force between two objects is inversely proportional to the square of their distance and directly proportional to their masses • F=(Gm1m2)/r^2 • (G= 6.67 x 10 ^-11 N x m^2/kg^2) • G represents the Universal Gravitational Constant Inverse Square Relationship • Distance between masses increases, gravitational force between objects decrease. • Example: (if the distance of two masses is doubled, the force is reduced to one forth the original value) • 2^2 = 4 then Find reciprocal value = ¼ Question 1 • A 120-N net force acts upon a 68-kg cart at rest. What acceleration results? Solution 1 • • • • a=F/m a= 120N/68kg a=(120 kg x m/s^2)/ (68kg) a=1.8 m/s^2 Question 2 • A force of F Newtons causes a mass of m kilograms to accelerate at 24 m/s^2. What acceleration would occur in the following conditions? • -the force is doubled to 2F Newtons and mass remains the same • -The force F Newtons is constant and the mass is tripled. Solution 2 • Acceleration is directly proportional to an object’s net force, therefore: • a=2(24 m/s^2)= 48 m/s^2 • Acceleration is inversley proportional to mass, when mass is tripled, there is a decrease in acceleration, thefore: • a= (24 m/s^2)/ 3 = 8 m/s^2 Question 3 • A 400-newton girl standing on a dock exerts a force of 100 Newton's on a 10,000-newton sailboat as she pushes it away from the dock. How much force does the sailboat exert on the girl? • Mass of Earth= 5.98 x 10^24 kg • Mass of moon= 7.35 x 10 ^22 kg • Distance= 3.84 x 10 ^8 m Solution 3 • Newton’s Third Law: For every action there is an equal and opposite reaction. • Since the girl is applying a force of 100 N on the sailboat, the sailboat is applying a force of 100 N back to her. • Answer: 100 N Question 4 • What is the mass of a 100-N Weight? Solution 4 • • • • g= F/m m=F/g m= (100 kg x m/s^2)/(9.81 m/s^2) m= 10.2 kg Question 5 • Which cart has the greatest Inertia? • • • • A-speed of 4 m/s and 1 kg load B-Speed of 3 m/s and 2kg load C-Speed of 1.5 m/s and 3 kg load D-Speed of 1 m/s and 4kg load Answer • Choice D • The greater the mass, the more inertia.