Maximum Height of Lighter Object in Pulley System - Homework Solution

[joseg707]

Homework Statement

Two masses, 3.2kg and 2.2kg are each initially 1.80m above the ground, and the massless and frictionless pulley is 4.8m above the ground. What maximum height dies the lighter object reach after the system is released? Assume it doesn't hit the pulley.

Homework Equations

F=ma
y=y_o+v_o+1/2at²

The Attempt at a Solution

I solved for acceleration by using F=ma and got 1.8m/s².
I then solved for the velocity of the lighter object when the heavier object hit the ground by solving for the time it took for the heavier object to hit the ground and used that time to find the velocity

-1.8=-0.9t²
t=1.4

v=1.8*1.4
v=2.56

After finding the velocity I used that to find the maximum height.

y=2.56t-4.9t²
t=0, 0.522

0.522/2
t=0.261

y=3.6+2.56t-4.9t²
y=3.93333

I think I didn't take something into account or I used the wrong equation completely. Can someone help me?

 

[Redbelly98]

Looks good to me.

 

[nlightner]

I would like to commend you on your attempt at solving this problem. Your use of the equations F=ma and y=yo+vo+1/2at2 are correct in finding the acceleration and velocity of the lighter object. However, it seems like you may have made a mistake in your calculation for the time it takes for the heavier object to hit the ground. It should be t=1.4 seconds, not 1.4 meters. This means that your calculation for the velocity of the lighter object is also incorrect.

To find the maximum height of the lighter object, you can use the equation y=yo+vo+1/2at2, where yo=1.8m, vo=0, a=-1.8m/s2, and t=1.4 seconds.

y=1.8+0+1/2(-1.8)(1.4)2
y=1.8+0.882
y=2.682m

Therefore, the maximum height reached by the lighter object is 2.682m.

One thing to note is that this solution assumes no external forces acting on the system, such as air resistance. In real-world situations, these external forces may affect the accuracy of the calculated maximum height. Overall, your approach to solving this problem was correct, but be sure to double check your calculations for accuracy.