Variables in a centripetal motion problem

[dominus96]

Homework Statement

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?

Homework Equations

h = v0t + gt^2/2

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?

 

[tyco05]

Here's a hint:

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

 

[dominus96]

It would be 0, correct?

So then h = gt^2/2

And so t = sqrt(2h/g)

Is that right?

 

[tyco05]

Sounds good to me.

 

[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

 

[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).

 

[dominus96]

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

 

[learningphysics]

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

Yes, it is here.