Question

A cable with $20.0N$ of tension pulls straight up on a $1.50kg$ block that is initially at rest. What is the block’s speed after being lifted $2.00m$? Solve this problem using work and energy.

Short answer

The block's speed =$7.302m/s$.

Step-by-step solution

Speed : 

It is the change in an object's location with regard to time.

Explanation : 

Rope's tension $T=20N$

block's mass$m=1.5kg$

lift of h = $2m$

Work done is,

$W=T\times h$

Block's kinetic energy is calculated by,

$KE=\frac{1}{2}m{v}^2$

$KE$= kinetic energy

$m$= block's mass

$v$= block's velocity

To lift the block upto $2m$, the work required is,

$$\begin{gathered} W=T\times h \\ W=20\times 2 \\ =40J \end{gathered}$$

Since the work is done to increase the block's potential energy, the change in potential energy equals the change in kinetic energy, according to the law of energy conservation.

$KE=W$

Block's velocity after being lifted for $h=2m$is,

$$\begin{gathered} \frac{1}{2}m{v}^2=KE=W \\ \frac{1}{2}\times 1.5\times v^2=40 \\ v=7.302m/s \end{gathered}$$

Hence, block's velocity is$7.302m/s$.