# Variables in a centripetal motion problem

1. Oct 30, 2007

### dominus96

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

An object of mass M on a string is whirled in a horizontal circle. When the string breaks, the object has the speed v0, the circular path is radius R, and the height of the object above the ground is h.

In terms of h, v0, and g, what is the time it takes for the object to hit the ground?

2. Relevant equations

h = v0t + gt^2/2

3. The attempt at a solution

I honestly don't know where to begin. I have the equation, and need to solve for time (t) but don't know how to get that variable isolated. Is there some other formula I need?

2. Oct 30, 2007

### tyco05

Here's a hint:

If the mass is being whirled in a horizontal circle, then what is its vertical velocity?

3. Oct 30, 2007

### dominus96

It would be 0, correct?

So then h = gt^2/2

And so t = sqrt(2h/g)

Is that right?

4. Oct 30, 2007

### tyco05

Sounds good to me.

5. Oct 30, 2007

### dominus96

Thank you, but I have 2 more parts to the problem I need to solve.

(a) What is the horizontal distance it travels? (using h, v0, and g again)

(b) Determine the tension in the string just before it breaks.

For part (a) I know S = vt, and I can use my t that I just solved for. But what would be my horizontal velocity (v)?

And for part (b) all I know is F=ma, but don't know how to find the tension. This is the free-body:

Tension
O------------>
l
l
l <-Weight
l
v

6. Oct 30, 2007

### tyco05

a) It gives you the horizontal velocity in the question (speed).

b) Do you know anything else about circular motion? Centripetal acceleration is what you need for this one. Then apply F = ma to this acceleration to find the force (tension).

7. Oct 30, 2007

### dominus96

Ok I got a but I'm still confused about b. Is the tension the same as the centripetal force?

8. Oct 30, 2007

### learningphysics

Yes, it is here.