# Newtons Laws

1. Sep 16, 2007

### BuBbLeS01

1. The problem statement, all variables and given/known data
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

3. 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.

2. Sep 16, 2007

### 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.

3. Sep 16, 2007

### 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?

4. Sep 16, 2007

### BuBbLeS01

less than

5. Sep 16, 2007

### arildno

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

6. Sep 16, 2007

### BuBbLeS01

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

7. Sep 16, 2007

### arildno

Correct!

8. Sep 16, 2007

### BuBbLeS01

Thank you!

9. Sep 16, 2007

### arildno

You are not finished..

10. Sep 16, 2007

### 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

11. Sep 16, 2007

### arildno

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

The other relations are right.

12. Sep 16, 2007

### BuBbLeS01

okay thanks so much!