**QUESTION**

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The suggested time is about 15 minutes for the question. Read each part carefully. Show all your work for each part of the question. The parts within the question may not have equal weight. Figure 1 Students are performing an experiment with the setup shown above, where a block of mass $M$ sits on a horizontal table. The coefficient of kinetic triction between the block and the table is $\mu_{k}$. The block is connected to a hanging object over a pulley. The pulley has negligible mass and friction. The string connecting the two is very light and does not stretch. The students add mass to the hanging object so that its mass is $m$, where $m<M$, and the block-hanging object system is released from rest. The hanging object falls for a distance $h$, at which point it collides with the ground and comes to rest. The block on the table keeps sliding and travels a total distance $d$ before coming to rest. It does not reach the pulley, and $d>h$. (a) If the experiment were repeated where the height $h$ above the floor was increased, would the distance that the block slides after the hanging object hits the foor increase, decrease, or remain the same? Justify your answer without using or manipulating equations. Students derive the following equation for the relationship between the distance $d$ and the height $h$. \[ (d-h)=\frac{h\left(m-\mu_{1} M\right)}{\mu_{1}(M+m)} \] (b) Whether or not this equation is correct, does it match your reasoning in part (a)? Justify your answer.

(c) Students notice that the acceieration due to gravily does not appear in the equation above and assume that must be a mistake. Do you agree with them? Justify your answer. A student creates the following data table for the net force exerted on the block during the speeding up and slowing down portions of the experiment. \begin{tabular}{|l|l|} \hline Net force ons) Ispeeding upl & Net force (N) (Slowing downl \\ \hline $8 \mathrm{~N}$ & $-2 \mathrm{~N}$ \\ \hline \end{tabular} (d) Does the block of mass $M$ spend more time speeding up or slowing down? Justify your answer: Figure 2 (e) Students create the graph of net force on the block as a function of postion for the block as shown above in Figure 2 but neglect the horizontal scale. If the students were to use an accurate horizontal scale, would the area under the force graph marked Area 1 be greater than, less than, or equal to the area under the force graph marked Area 2? Justify your answer. (f) At the beginning of the final triat, the string connecting the hanging object and the block is cut. The hanging object collides elastically wth the foor and bounces vertically. Describe how high is bounces in terms of $h$. Justify your answer.