PHYS100+Midterm+2018+(standard+sitting)+solutions (1).pdf

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PHYS100 Midterm 2018 (standard sitting) solutions Note: There were four different versions of this midterm. You likely noticed whilst writing the midterm that two of your multiple choice questions were split into two parts. The second part asked you to explain your reasoning to the first. Each version of the midterm had this part in a different pair of multiple choice questions, (respectively A3, A4, A5, and A6). The solutions to all those parts are provided together here in this solution document. Multiple Choice A1 Ball 1 is thrown straight up in the air and at the same instant ball 2 is released from rest and allowed to fall. (Take“up” as the positive direction.) Part a) [2 pts] Question : Which velocity graph in the figure best represents the motion of the two balls? Answer : A . Explanation : We know that after the balls have been thrown, the only force acting on them is gravity. Since gravity is pointing downward, and we are told in the problem that “up” is positive, that means acceleration is negative, so the slope of our velocity-time graph should be negative and constant (because acceleration due to gravity is always 9.8 m/s 2 ). The fact that is must be constant eliminates C : the fact that it is negative eliminates B . Since initially one of the balls had a positive velocity (it was thrown upward), at time 0 one of the velocities (that of ball 1) must be positive — only option A satisfies all these. A2 [2 pts] Question : As shown in the figure, a woman is straining to lift a crate, but cannot lift it because it is too heavy. We denote the forces on the crate as follows: P is the magnitude of the upward force being exerted on the crate by the person, N is the magnitude of the normal force on the crate from the floor, and W is the weight of the crate. How are the magnitudes of these forces related while the person is trying unsuccessfully to lift the crate? (A) P + N = W (B) P + N < W (C) P + N > W (D) P = N 1

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Figure 1: Figure for A1. Answer : A . Explanation : Since there are only three forces acting on the box, and the box is not moving — that is, it is not changing its velocity from zero to some nonzero value (since its acceleration is zero) — that means that the forces acting on the box must be balanced. So we cannot have the inequalities from B or C : if this was the relationship between the forces, the box would start moving, either up or, even worse, down through the floor. Since we know that the weight is acting downwards, we are left with choice A . A3 Consider the following situations, where two sled dogs are each trying to pull their own heavy sled. Each dog pulls with the same pulling force, F pull , but is unsuccessful in moving their sled. Thus, the sleds remain at rest in both situations. The total mass of the sled in situation 2 is half as large as in situation 1.

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