# Potential Energy and Kinetic Energy

• Manh

## Homework Statement

Two blocks are hung by a string draped over a pulley, a 1.5-kg block on the left and a 3.0-kg block on the right. The two blocks start out at rest and at the same height.

A. What is the change in the gravitational potential energy of the system of blocks and Earth when the 3.0-kg block has dropped 0.60 m ?
B. What is the change in the kinetic energy of the system between release and this instant?
C. What is the velocity of the 1.5-kg block at this instant?

U = m*g*h
K = 1/2 m*v^2

## The Attempt at a Solution

A. U = (3.0 kg)(9.8 m/s^2)(0.60)
= 17.64 J
I wonder if the answer should have a negative sign!

B. K = 17.64 J
Since U is converted to K, therefore K has the same value of U. Am I correct?

C. 17.64 = 1/2*(1.5)*v^2
v = 4.85 m/s
These are my works and answers. I hope somebody can help me check them. Thanks!

A. U = (3.0 kg)(9.8 m/s^2)(0.60)
= 17.64 J
I wonder if the answer should have a negative sign!
Don't ignore the movement of the 1.5 kg mass. (As far as sign, when something lowers the change in gravitational PE is negative.)

B. K = 17.64 J
Since U is converted to K, therefore K has the same value of U. Am I correct?
Yes, but you have the wrong value. (See A.)

C. 17.64 = 1/2*(1.5)*v^2
v = 4.85 m/s
These are my works and answers. I hope somebody can help me check them. Thanks!
Realize that the total kinetic energy is for both masses.

Don't ignore the movement of the 1.5 kg mass. (As far as sign, when something lowers the change in gravitational PE is negative.)
A. U1 = (1.5 kg)(9.8 m/s^2)(0.6 m) = 8.82 J
U2 = (3 kg)(9.8 m/s^2)(-0.6 m) = -17.64 J
delta U = -17.64 J + 8.82 J = -8.82 J
Yes, but you have the wrong value. (See A.)
B. delta K = 8.82 J
Realize that the total kinetic energy is for both masses.
C. K = 1/2 m1*v1^2 + 1/2 m2*v2^2. Where K = 8.82 J. Is this correct?

C. K = 1/2 m1*v1^2 + 1/2 m2*v2^2. Where K = 8.82 J. Is this correct?
Yes, but what is the relationship between the two velocities?

wouldn't you end up with 2 variables v1 and v2?