**QUESTION**

Text

Image

A small block of mass slides on a horizontal surface where friction between the block and the surface is negligible as it travels around the inside wall of a hoop of radius $R$. The coefficient of friction between the block and the wall is $\mu_{k}$. The block is given an initial speed $v_{0}$ tangent to the hoop and allowed to travel along the inside edge. (a) The block is allowed to travel around the hoop for a time $t_{1}$. At that moment the speed of the block is $v_{1}$. The experiment is repeated but the initial speed of the block in the second trial is greater than $v_{0}$. Will the speed of the block after a time $t_{1}$ be greater than, less than, or equal to $v_{1}$ ? Justify your answer. Please respond on separate paper, following directions from your teacher. (b) Students derive the following equation for the speed of the block as a function of time: $\frac{1}{v(t)}=\frac{\mu_{k} t}{R}+\frac{1}{v_{0}}$. Whether or not this equation is correct, does it match your claim in part (a)? Justify your answer. Please respond on separate paper, following directions from your teacher.

(c) Briefly describe how students could use the equation from part (b) to derive an equation for the tangential acceleration of the block as a function of time. Please respond on separate paper, following directions from your teacher. (d) Without deriving equations, describe what will happen to the angular momentum of the block with respect to the center of the hoop as a function of time. Justify your answer. Please respond on separate paper, following directions from your teacher. Graph A Graph B Graph C (e) Students created the above graphs of the speed of the block as a function of time. Which of the labeled graphs correctly models the speed of the block as a function of time? Justify your answer. Please respond on separate paper, following directions from vour teacher.

(f) Describe briefly the relationship between the magnitude of the centripetal force on the block and the magnitude of the normal force applied by the hoop on the block. Justify your answer.