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HW 6 Solutions - Solution for Long-answer Homework 6...

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Solution for Long-answer Homework 6 Inertia and Momentum problems Solution to Long-answer Homework Problem 6.1() Problem: How does friction between a stationary surface and an object moving with respect to the surface affect the velocity of the object in motion? (Just consider this for sliding, no rolling motion here-interesting stuff happens when we study that later.) Solution It slows it down. Friction always opposes (is in the opposite direction of) the relative motion of two objects, or an object and the “surface” it is interacting with. Consider air, if the air is stationary and you try to move through it, the friction will always cause you to slow down. However, if the wind is blowing faster than you are moving, it is like you are pushing backwards on it, so it pushes you forward, speeding you up! 1 point(s) : On this homework, just give 1/2 point if they tried this problem. Total Points for Problem: 1 Points Solution to Long-answer Homework Problem 6.2() Problem: Suppose that you have an object with inertia 2kg and another with an unknown inertia. How can you use the definition of inertia to solve for the unknown inertia? The easiest way to show this might be to start with an accepted mathematical equivalent for this definition from the textbook, and rearrange it to isolate the unknown inertia. Briefly describe what quantities you would need to measure (no scales or balances or any other direct measurement of inertia allowed). Solution There are several equations that represent the definition of inertia. I will pick the closest one to what I want, to save a few steps, but any is equally acceptable. One of the representations of inertia is that: m = - Δ vectorv std Δ vectorv m std where m std would be 2kg since we have a m known = 2kg . We can collide the two objects, measure the change in both velocities, and then solve for m in m = - Δ v std Δ v m std = - Δ v std Δ v 2kg . 1 point(s) : For this homework, we are looking for chose a correct math- ematical representation of the law of inertia, and said some words about measuring either v or Δ v according to which definition they chose. If they only did one of these things, they only get 1/2 point. Total Points for Problem: 1 Points Solution to Long-answer Homework Problem 6.3() Problem: Consider an object moving at v = +40 m s and having an inertia of m = 10kg . 1
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(a)What is this object’s momentum? Is it a vector or scalar quantity? (b)If it hits an unknown object and its momentum is cut in half, what is the change in momentum of both objects? (c)If the original object hits a stationary object with inertia m = 5kg and gives it a velocity of v = +10 m s , what would the original object’s final velocity be? Solution to Part (a) Linear momentum is given by vector p = mvectorv .
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