91Ó°ÊÓ

A body accelerates when a net force acts on it and travels in the same direction as the net force. The product of mass and acceleration vector is equal to the force vector.

$∑\stackrel{→}{F}=m\stackrel{→}{a}$

Here tension in the rope will pull the crate upward, and the force of gravity will pull it downward. At rest or moving at constant speed upward, the acceleration is zero.

T - mg = 0

T= mg

The tension is equal to the weight of the crate.

When speeding up at an acceleration a, the tension in the rope is

T + (-mg)=ma

T = m(g + a)

When it slows down, the crate is de-accelerating; therefore, it will have a negative sign.

T + (-mg)=m(- a)

T = m(g - a)

It is apparent from the obtained results that tension in the rope will be greater when speeding up than when slowing down.