Pulley with Kinematics in One Dimension Question

[jakecar]

Homework Statement

Two masses hanging vertically from a pulley are each initially 1.6 m above the ground and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released?

Homework Equations

$$\vec{F}_{net} = \Sigma \vec{F} = m \vec{a}$$

$$v = v_0 + a t$$

$$x = x_0 + v_0 t + (1/2) a t^2$$

$$v^2 = v_0^2 + 2 a \Delta x$$

The Attempt at a Solution

I already found the acceleration to be $$4.45\frac{m}{s^2}$$. Now I know that I have to figure out how high the lighter mass goes when the heavier mass is on the ground. The problem for me is that I can't find time t, velocity v, or final position x. Also, where does the given height of the pulley (4.8 m) come into play? Thanks for any help.

 

[Doc Al]

I presume you are given the two masses? In any case, what happens after the lower mass hits the ground?

 

[jakecar]

One mass is 1.2 kg and the other is 3.2 kg. After the heavier mass hits the ground, the lighter mass stops at some unknown height. The lower mass never hits the ground. I can't seem to figure out how much time it takes for the heavier mass to hit the ground or with what velocity it hits the ground either.

 

[Doc Al]

One mass is 1.2 kg and the other is 3.2 kg. After the heavier mass hits the ground, the lighter mass stops at some unknown height.

When the heavier mass hits the ground, what happens to the force (and acceleration) of the lighter mass? (What happens to the tension in the string?)

The lower mass never hits the ground.

I meant lower in height, not mass.

I can't seem to figure out how much time it takes for the heavier mass to hit the ground or with what velocity it hits the ground either.

Why not? You have the acceleration and the distance traveled. You can also use energy conservation to find the final speed. (No need to find the time.)

 

[jakecar]

I don't think I'm supposed to use energy conservation because we haven't learned that yet and it's not in the chapter that we're currently on. Using the kinematics equations, I can figure out the velocity of the lighter mass when it reaches the pulley if there was no ground. How can I use that information to figure out the maximum height of the lighter mass? How is the tension of the string related? Thanks for the help :)

 

[Doc Al]

Using the kinematics equations, I can figure out the velocity of the lighter mass when it reaches the pulley if there was no ground.

Find the speed of the masses when the heavy one hits the ground.

How can I use that information to figure out the maximum height of the lighter mass? How is the tension of the string related?

If the string stopped pulling on the lighter mass, what would its acceleration be?