If the blocks $m_1=2.4 \mathrm{~kg}$ and $m_2=1.1 \mathrm{~kg}$ are to travel a distance $d=6.5 \mathrm{~cm}$ before coming to rest Assume the coefficient of kinetic friction between $m_1$ and the tabletop is $\mu_{\mathrm{k}}=0.25$. Find the work done on $m_2$ by the rope.

The two blocks are moving with an initial speed $v$. Is the work done on block 2 by the rope positive, negative, or zero? Explain.

The two blocks are moving with an initial speed $v$. (a) If the system is frictionless, find the distance $d$ the blocks travel before coming to rest. (Let $U=0$ correspond to the initial position of block 2.)

An ice cube is placed on top of an overturned spherical bowl of radius $r$, as indicated in Figure 8-30. If the ice cube slides downward from rest at the top of the bowl, at what angle $\theta$ does it separate from the bowl? In other words, at what angle does the normal force between the ice cube and the bowl go to zero?

Suppose that $L=0.652 \mathrm{~m}$ and $l=0.325 \mathrm{~m}$ . Calculate the maximum angle the string makes with the vertical when the mass is released from rest at point $A$ and swings as far to the right as it can.) Give the angle as a general expression in terms of $L$ and $l$.

Suppose that $L=0.652 \mathrm{~m}$ and $l=0.325 \mathrm{~m}$ . Calculate the maximum angle the string makes with the vertical when the mass is released from rest at point $A$ and swings as far to the right as it can.) At the point found, find the height of the mass above point $B$. Explain the physical significance of your result.