Question

A block of mass 2 kg is suspended by a light thread from an elevator. The elevator is moving upward with constant speed 4 m/s. The work done by tension on block w.r.t ground in 3 seconds is

Answer 1

Given :

mass (m) = 2 Kg

velocity (v) = 4 m/sec

time (t) = 3 sec

To Find :

The work done by tension on block w.r.t ground in 3 seconds

Solution :

As the elevator is moving with a constant velocity, hence acceleration = 0

No pseudo force is acting on the block.

So, Tension (T) = mg (where m = mass; g = acceleration due to gravity)

                    T  = 2 × 10 = 20 N

Displacement (ds) = 4 × 3 = 12 m

Work Done = Force × Displacement

                   = 20 × 12

                  = 240 J

∴ The work done by tension on block w.r.t ground in 3 seconds is 240 J.

Answer 2

Given:

Mass of the block (m) = 2 kg

Speed of elevator (v) = 4 m/s

Time (t) = 3 s

To find:

Work done by tension.

Solution:

We have been given that a block is suspended by a light string connected to the elevator and the elevator is moving upwards, hence, the dominant force here, will be the tension in the string , which is given by

$T-mg=ma$   $;$ $or$

$T=m(g+a)$    $(i)$

It is also given that the elevator is moving at a constant velocity (Δ$v$ $= 0$)

Hence, the acceleration will be

$a=\frac{dv}{dt}$  $;$ $or$

$a=0m/s^{2}$  

Therefore, the tension in the string will only be due to acceleration due to gravity, that is

$T=mg$

Substituting the values

$T=2(10)$  $;$ $or$

$T=20N$

We know, the speed with which elevator is going upwards that is $v=4m/s$ and we also know the acceleration is 0 hence, distance traveled in 3 s is

$s=ut+\frac{1}{2}at^{2}$

$s=ut$

Substituting the given values in equation, we get

$s=(4)(3)$

$s = 12m$

Hence, the elevator travels $12 m$ in $3 s.$

Therefore,

The work done by tension will be

$W=Fs$     $;$ $here$, $F=T$

$W=Ts$  

Substituting the given values, we get

$W=20(12)$

$W=240J$

Final answer:

Hence, the work done by tension on the block will be $240J$.