A block of mass M is at rest on a table. It is connected by a string and pulley system to a block of mass m hanging off the edge of the table. Assume the hanging mass is heavy enough to make the resting block move. If the acceleration of the system and the masses of the blocks are known, which of the following could NOT be calculated?
A) Net force on each block
B) Tension in the string
C) Coefficient of kinetic friction between the table and the block of mass M
D) The speed of the block of mass M when it reaches the edge of the table
A) Net force on each block
B) Tension in the string
C) Coefficient of kinetic friction between the table and the block of mass M
D) The speed of the block of mass M when it reaches the edge of the table
The net force on each block can be found by using Newton’s Second Law,
$$F_{\mathrm{Net}}=ma$$
The tension in the string can be found by focusing on the hanging mass. You know the net force on it will be
$$F_{\mathrm{Net}}=ma=F_{\mathrm{g}}-T=(mg)-T$$
which means
$$T=(mg)-(ma)$$
Finally, the coefficient of kinetic friction can be found by the looking at the top block. For that block, the net force in the horizontal direction will be the same as the overall net force since the two vertical forces (normal and gravity) will cancel out. Thus, you get
$$F_{\mathrm{Net}}=ma=T-F_{\mathrm{f}}=T-\mu FN=T-\mu mg$$
The only value in the answers you cannot calculate is the speed of the block when it reaches the edge. In order to compute this value, you would need to know how far from the edge the block is when it begins moving.