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Hmwk_04_Solutions - Physics 221 Fall 2008 Homework#4...

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1 Physics 221 Fall 2008 Homework #4 Solutions Chs. 4 and 5:1,2 Due Tues, Sept 23, 2008 4.1 (a) State Newton’s three laws of motion in words. What is an “inertial reference frame” and how is an inertial reference frame related to Newton’s laws? 1 st Law: A particle moves at constant velocity in the absence of a net force on it. 2 nd Law: The acceleration of a particle is given by the net force on the particle divided by its mass. 3 rd Law: If object A exerts a force on object B, then object B exerts a force on object A with the same magnitude and with the opposite direction. An inertial reference frame is, by definition, a reference frame in which Newton’s laws are valid. Such a reference frame is either at rest or moving with constant velocity with respect to the distant stars. (b) Why is Newton’s 1 st law stated as a separate law? Isn’t it just a special case of Newton’s 2 nd law? Newton’s 1 st law says nothing about the concept of mass and does not need the concept of mass for a statement of the law or use of the law. To this extent the 1 st law is independent of the 2 nd law. On the other hand, putting the acceleration equal to zero in the 2 nd law gives the 1 st law, so in this sense the 1 st law can be considered to be a special case of the 2 nd law. (c) You hold an ideal massless spring horizontally that pushes on an identical horizontal spring attached to a cart on a horizontal surface, and by this means you accelerate the cart. You exert a force on the cart via the spring you hold and the cart exerts a force back on you via the spring attached to the cart. Because these two forces add to zero, how can the cart ever accelerate? How can you tell if Newton’s 3 rd law is obeyed while the cart is accelerating? Newton’s 2 nd law refers to the net force on a single object. The force of the cart on you is not part of the net force on the cart. Therefore there is no paradox. You can tell if Newton’s 3 rd law is obeyed by looking at the compressions of the two springs. If they are the same, then that means that the magnitude of the force you are exerting on the cart is the same as the magnitude of the force the cart is exerting on you. (d) A big truck and a small car collide head-on. According to Newton’s 3 rd law, during each instant of the collision the magnitude of the force of the car on the truck is identical to the magnitude of the force of the truck on the car. Then why is a passenger safer in the big truck than in the small car even if both are equally sturdy? Hint: What is the magnitude of the force on a passenger in each vehicle during the collision? The big truck has a much larger mass than the small car, and hence the magnitude of the acceleration of the truck is much smaller than that of the car during the collision. What is important for a passenger’s safety is the force on the passenger, not the force on the vehicle.
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