Understanding Tension and Weight in Elevators: Newton's Laws Homework

[BuBbLeS01]

Homework Statement

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.)

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

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

The elevator is stationary and remains at rest.

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

The elevator is traveling upward at a constant velocity.

The elevator is traveling downward and its downward velocity is increasing

The Attempt at a Solution

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

Where am I going wrong? My answers are not right, but I am not sure where my mistake(s) are.

 

[genneth]

Draw diagrams showing a ball and three things: the tension, the weight, and the acceleration. Apply Newton's 2nd law F=ma and try to deduce the relations.

 

[arildno]

Take the first one:
In this case, acceleration is DOWNWARDS, in the direction of the force of gravity.
Now, does that mean the upwards tension force is greater or less than the weight of the mass?

 

[BuBbLeS01]

less than

 

[arildno]

Quite so!
Now, give an argument as to why you think 2. is correct.

 

[BuBbLeS01]

because the acceleration is acting upwards, opposite of gravity so the tension force would be greater

 

[arildno]

Correct!

Now, study your other answers, present your arguments for your view; you are allowed to change your mind if you think you made some mistake earlier.

 

[BuBbLeS01]

Thank you!

 

[arildno]

You are not finished..

 

[BuBbLeS01]

I know I am working on them... I know the third has to be equal and the 4th I think T would be greater because it is accelerating upwards, opposite of gravity

 

[arildno]

I know I am working on them... I know the third has to be equal and the 4th I think T would be greater because it is accelerating upwards, opposite of gravity

You are right; only a "surplus" of tensile force can yield upwards acceleration.

The other relations are right.

 

[BuBbLeS01]

okay thanks so much!