Question

bailof mass M is suspended by a thin string (of negligible mass) from the ceiling of an elevator. The vertical motion of the elevator as it travels up and down is descnibed in the statements below. Indicate for each of the situations described the relation between value of the tension in the cable, T, and the weight of the ball, Mg, or whether one Cannot teil. (Assume that there is no air, .e., neglect the buoyancy effect of the air) Loui-V] The elevator is traveling upward and its upward velocity is decreasing as it nears a stop at a higher noor ram-コThe elevator is traveling downward and its downward veiocity is decreasing as it nears a stop at a lower floor. M The elevator is traveling upward and its upward velocity is increasing as it begins its journey towards a higher floor The elevator is traveling downward and ts downnward velocity is increasing The elevator is stationary and remains at rest The elevator is traveing downward at a constant velocity Think "Newton's 1st and 2nd Laws". Do not confuse "motion·wsh "acceleration", Motion can occur wth and without acceleration.

Answer 1

The forces acting on ball in elevator are

Tension
The forces acting on ball in elevator are Tension T upwards and weight of the ball mg downwards. The elevator is travelling upward and its upward velocity is decreasing as it nears to stop at a higher floor As the upward velocity is decreasing, the body is moving up with an acceleration -a Net force acting on the ball is T - mg = -ma (or) T = m(g - a) and so T < mg The elevator is travelling downward and its downward velocity is decreasing as it nears to stop at a lower floor As the downward velocity is decreasing, the body is moving down with an acceleration -a Net force acting on the ball is mg - T = -ma (or) T = m(g + a) and so T > mg The elevator is travelling upward and its upward velocity is increasing as it begins its journey towards a higher floor +a Net force acting on the ball is T - mg = ma
upwards and weight of the ball downwards.

i) The elevator is travelling upward and its upward velocity is decreasing as it nears to stop at a higher floor

As the upward velocity is decreasing, the body is moving up with an acceleration

Net force acting on the ball is $T-mg=-ma$ (or) $T=m(g-a)$ and so

ii)

The elevator is travelling downward and its downward velocity is decreasing as it nears to stop at a lower floor

As the downward velocity is decreasing, the body is moving down with an acceleration

Net force acting on the ball is $mg-T=-ma$ (or) and so

iii)

The elevator is travelling upward and its upward velocity is increasing as it begins its journey towards  a higher floor

As the upward velocity is increasing, the body is moving up with an acceleration

Net force acting on the ball is (or) and so

iv)

The elevator is travelling downward and its downward velocity is increasing.

As the downward velocity is increasing, the body is moving down with an acceleration

Net force acting on the ball is $mg-T=ma$ (or) $T=m(g-a)$ and so  

v)

The elevator is stationary and remains at rest

Net force acting on the ball is $T-mg=0$ , (or)

vi)

The elevator is moving downward at constant velocity

Constant velocity means zero acceleration.

Net force acting on the ball is $mg-T=0$ , (or)