Question

A block of mass m is suspended by a light thread from an elevator. The elevator is accelerating upward with uniform acceleration ‘a’. Find the work done during the first ‘t’ seconds by the tension in the thread.

Answer 1

A block of mass m is suspended by a light thread from an elevator. the elevator is accelerating upward with uniform acceleration ‘a’.
we know, Newton's law doesn't valid in non-inertial frame of reference. so, we have to add Psuedo force just opposite direction of it motion to make inertial frame of reference.
so, tension in the thread = mg + ma→ [ Psuedo force]
tension = m(g + a)

now, we have to find displacement of elevator.
use formula, S = ut + 1/2 At²
here A is net acceleration acts on elevator.
here u = 0, A = a [ upward direction]
so, S = 0 + 1/2 at²
hence, displacement is 1/2at²

now, workdone = Tension × displacement
= m(g + a) × 1/2 at²
= 1/2 m(g + a)at² Joule

Answer 2

Tension in the thread = mg+ma,

Where, ma is pseudo code,

since we know that Newton’s law work in case of non inertial frame so,

we have to add pseudo code to make it inertial frame,

Tension = m(g+a),

To find elevator displacement,

use s= ut+1/2at2 formula,U=0,

s= 0+1/2at2,

So displacement is 1/2at2,

Workdone= tension x displacement,

=m(g+a) x 1/2at2,

=1/2m(g+a)at2 Joule