NTSG-CRT74: HANGING STONE CONNECTED TO A SLIDING BOx-VELOCITY VS. TIME A box is
ID: 776551 • Letter: N
Question
NTSG-CRT74: HANGING STONE CONNECTED TO A SLIDING BOx-VELOCITY VS. TIME A box is sliding to the right along a horizontal surface with a velocity of 2 m/s. There is friction between the box and the horizontal surface. The box is tied to a hanging stone by a massless rope running over a massless, frictionless pulley. The mass of the stone is larger than the mass of the box. The box will slow down, come to rest at an instant, and then move to the left with increasing speed. Assume that a positive velocity represents motion to the right. v=2m/s 240 g Which, if any, of the velocity versus time graphs below represent the movement of the sliding box? A AVelocity B AVelocity C AVelocity Time Time Time D AVelocity E AVelocity F AVelocity Time lime ime Explain.
Explanation / Answer
mass of stone = M
mass of box = m
for box
T + fk = m*a1
for stone
Mg - T = M*a1
Mg + fk = a1(M+m)
a1 = (Mg+fk)/(M+m
on the box the acceleration acts to the left ( -x axis)
the initial velocity is to the right ( + x axis)
velocity and acceleration are opposite
the velocity decreases as the moves to left and becomes 0 at some instant
and the velocity increases along -x axis
as the box moves left
T - fk = m*a2
for stone
Mg - T = M*a2
Mg - fK = a2*(M+m)
a2 = (Mg - fk)/(M+m)
a2 < a1
the correct graph is OPTION D
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