Potential Energy and Kinetic Energy

In summary, two blocks of masses 1.5 kg and 3.0 kg are hung by a string over a pulley and start at rest and the same height. The change in gravitational potential energy of the system when the 3.0-kg block drops 0.60 m is -8.82 J. The change in kinetic energy of the system between release and this instant is also 8.82 J. The velocity of the 1.5-kg block at this instant is 4.85 m/s. However, the total kinetic energy for both masses must be considered, and the relationship between the two velocities needs to be determined.
  • #1
Manh
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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?

Homework Equations


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!
 
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  • #2
Manh said:
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.)

Manh said:
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.)

Manh said:
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.
 
  • #3
Doc Al said:
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
Doc Al said:
Yes, but you have the wrong value. (See A.)
B. delta K = 8.82 J
Doc Al said:
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?
 
  • #4
Manh said:
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?
 
  • #5
wouldn't you end up with 2 variables v1 and v2?
 

FAQ: Potential Energy and Kinetic Energy

What is potential energy?

Potential energy is the stored energy an object possesses due to its position or configuration. It is the energy that an object has the potential to release and convert into other forms of energy.

What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is dependent on the mass and velocity of the object, and is the result of the object's potential energy being converted into motion.

What is the relationship between potential and kinetic energy?

Potential and kinetic energy are interrelated and can be converted into one another. When an object is at rest, it has potential energy. When it is in motion, the potential energy is converted into kinetic energy. The total energy of an object is the sum of its potential and kinetic energy.

How is potential energy calculated?

Potential energy is calculated using the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height or distance of the object from a zero reference point. The unit of potential energy is Joules (J).

How is kinetic energy calculated?

Kinetic energy is calculated using the formula KE = 1/2mv^2, where m is the mass of the object and v is the velocity of the object. The unit of kinetic energy is also Joules (J).

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