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 and down is described 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 tell. (Assume that there is no air, i.e., neglect the buoyancy effect of the air.)
Answers are either T<Mg, T>Mg, T = Mg, or cannot tell.

1.) The elevator is traveling upward and its upward velocity is decreasing as it nears a stop at a higher floor.

2.)The elevator is traveling downward and its downnward velocity is increasing

3.)The elevator is traveling upward at a constant velocity.

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

5.)The elevator is stationary and remains at rest.

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

Explanation / Answer

The weight of the object is a constant while T and the a of the elevator are variable. So the weight of the object is equal to the sum of the variable forces on the object m * g = T + m * a rearranging we get the tension in the cable in all cases is determined by T = m*g - m*a where a is the acceleration of the elevator. So if a is in the same direction as g the T will decrease and if a is in the opposite direction of g then T will increase. For convenience consider down positive and up negative. Of course if no a (a=0) then T=m*g. 3 years ago

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