9/7/2006ISP B1 Newton’s Third Law

9/7/2006ISP B2 Newton’s Third Law

9/7/2006ISP B3 Which vehicle exerts a greater force ― the tow truck or the car?

9/7/2006ISP B4 1.The law of inertia. An object in motion remains in motion with constant velocity if the net force on the object is 0. 2.Force and acceleration. If the net force acting on an object of mass m is F, then the acceleration of the object is a = F/m. Or, F = ma. 3.Action and reaction. For every action there is an equal but opposite reaction. Newton’s laws of motion Action means force.

9/7/2006ISP B5 force on B due to A force on A due to B Newton’s third law We will see that this is very hard to accept! It is just not common sense. That is why it took a great genius like Newton to figure it out. Whenever one object exerts a force on another object, the second object exerts an equal but opposite force on the first object. Forces always occur like this, in pairs. For every action there is an equal but opposite reaction.

9/7/2006ISP B6 Example – A collision

9/7/2006ISP B7 Playing catch with a medicine ball A throws the ball and B catches it.  four forces When A throws the ball he exerts a force on the ball (toward the right) and the ball exerts a force on him so he recoils (toward the left). A B When B catches the ball he exerts a force on the ball (toward the left to stop it) and the ball exerts a force on him so he is knocked back (toward the right). ► Newton’s third law for the throw ► Newton’s third law for the catch

9/7/2006ISP B8 Which vehicle exerts a greater force ― the tow truck or the car?

9/7/2006ISP B9 Forces obey Newton’s third law. We’ll consider two examples: The force of universal gravitation The spring force

9/7/2006ISP B10 Universal Gravitation --- an example of Newton’s third law

9/7/2006ISP B11 The Earth pulls the apple down (“action”). The apple pulls the Earth up (“reaction”). The two forces are equal (but opposite).

9/7/2006ISP B12 When does a scientific theory become accepted as true?

9/7/2006ISP B13 The force on the 1 kg mass is +3.3 x N. The force on the 5 kg mass is –3.3 x N. ( + means to the right, i.e., increasing x) For a laboratory measurement, the gravitational force is really very weak. Henry Cavendish, 1798 : first measurement of G

9/7/2006ISP B14 What makes g? 9.81 m/s 2

9/7/2006ISP B15 Weighing the Earth Calculate the mass of the Earth. The force of gravity on m is, by definition, its weight, By Newton’s theory of universal gravitation, the mass of the Earth, relying on the Cavendish measurement

9/7/2006ISP B16 The spring force ---another example of 3 rd law Suppose the spring is stretched beyond its equilibrium length by a length x. The force on the mass m 1 is F 1 = +kx.  (k = Hooke’s constant) The force on the mass m 2 is F 2 =  kx.  (  + means to the right; - means to the left.) The forces are equal but opposite.

9/7/2006ISP B17 Example One end of a spring is attached to a wall. When the other end is pulled with a force of 50 N, the spring is stretched by 3 cm. What force would be required to stretch the spring by 5.5 cm? Answer: 91.7 N Hooke’s law: The strength of a spring force is proportional to the displacement (extension or compression). F = k x where k is called Hooke’s constant for the spring.

9/7/2006ISP B18 The truck pulls to the right. According to Newton’s third law, the car pulls to the left with an equal force. So how can they start moving, or accelerate? A puzzle: Resolution: Consider each part separately, and don’t forget that other forces are also acting.

9/7/2006ISP B19 Which team will end up in the puddle? But aren’t the forces equal but opposite !? Resolution: Don’t forget that there are other forces acting. Each team exerts a force on the Earth, so the Earth exerts a force on the team (3 rd law!). The net force on either team is toward the left. A puzzle : Tug of War String tension Contact force

9/7/2006ISP B20 Momentum, p = mv Newton’s third law implies conservation of momentum. As vectors, p = m v. momentum = mass x velocity Total momentum is constant.

9/7/2006ISP B21 Momentum, p = mv Total momentum is conserved: Proof

9/7/2006ISP B22 A small car ( Cooper Mini ) collides with a big truck ( Mack ). Which is greater – the force exerted by the truck or the force exerted by the car? A puzzle … The two forces are equal. They must be, by Newton’s third law! equal

9/7/2006ISP B23 When does a theory become accepted as true? The law of conservation of momentum states that the combined momentum is constant when particles interact. It is verified by many experiments. Since momentum conservation is equivalent to Newton’s third law, the third law became an accepted fact: a law of nature not just a hypothesis.

9/7/2006ISP B24 Harold Edgerton’s high speed photograph of Wes Kessler kicking a football. The force exerted by the ball on the toe (reaction) is equal to the force exerted by the toe on the ball. Really hard to accept!

9/7/2006ISP B25 Quiz Question The planet is pulled toward the moon (and vice versa). Calculate the gravitational force on the planet.

9/7/2006ISP B26 When you walk or run, what forces occur? At constant velocity the horizontal force is 0 and you continue to move because of inertia. To accelerate, you push backward against the floor; the reaction force, which is a friction force exerted by the floor on your foot, pushes you forward. This reaction force may be hard to visualize, but imagine what would happen if you were on a frictionless surface – can’t accelerate!

9/7/2006ISP B27 Resolution: Consider each part separately, and don’t forget that there are other forces acting. So how can they start moving, or accelerate? A puzzle Horse and Cart The horse pulls the cart with a force A (to the right). According to Newton, the cart pulls the horse with a force –A (to the left).

9/7/2006ISP B28 The four fundamental forces Gravity Electromagnetic forces Strong nuclear force Weak nuclear force All the fundamental interactions obey conservation of momentum (verified by experiments), which is equivalent to Newton’s third law. Nature appears to be complex; but beneath the surface, nature is simple.