A ball of mass M is suspended by a thin string (of negligible mass) from the cei

Question

A ball of 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 an down is described in the statements below. Indicate for each of the situations described the relation between valuve of the tension in the cable, T, and the weight of the ball, Mg, or whether one cannot tell. (Assume that there is no air, i.e., neglect the buoyancy effect of the air.)

T<Mg, T>Mg, T=Mg, Cannot tell

1. The elevator is traveling upward at a constant velocity.

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

3. The elevator is stationary and remains at rest.

4. The elevator is traveling downward and its downward velocity is increasing.

5. The elevator is traveling upward and its upward velovity is decreasing as it nears a stop at a higher floor.

6. The elevator is traveling downward and its downward velocity is decreasing as it nears a stop at a lower floor.  

Explanation / Answer

1. T<mg
2. T=mg
3. T>mg
4. T>mg
5. T<mg
6. T=mg

i would like to point out that mg refers to the 'normal' weight of the ball when it isnt moving. this is important to note because tension T is always dependent on the weight of the ball. if a ball is freefalling, it should be weightless, ie, mg=0, therefore T should also be 0. what i am trying to say is that current T=current mg ALWAYS. but for the case of this question, mg refers to stationary mg, in which case, current tension need not always be equal to it.

you can imagine yourself in the elevator. as it starts to move up, you feel heavier for a second. if you were hung by a rope, that robe would be stretched more during that time (more tension). thus T>mg, or current tension in the rope is more than your usual weight. once the elevator starts moving at a constant upward speed, you're back to normal weight. that rope tension = your regular weight! as it starts to slow down at the top floor, you start to feel that weightless sensation...therefore the tension must be less than your usual weight.

due to newton's first law, F=ma, force, or tension in the rope is dependent on mass and acceleration. mass never changes. and velocity is not in the equation, only acceleration. so for #6 and #2, theres no added force on the rope except for the ball's mass and the gravity's acceleration.

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