What is the decrease in kinetic energy during the collision?

[mustang]

Problem 25.
A railroad car with a mass of 2.31*10^4kg moving at 3.59m/s collides
and joins with two railroad cars already joined together, each with
the same mass as the single car and initially noving in the same
direction at 1.34m/s.
b.What is the decrease in kinetic energy during the collision? Answer
in units of J.
Note: I find out that the final speed of the joined cars were 2.09m/s.
When I found the difference of kinetic energy I found the final kinetic energy by multiplying .5(2.31*10^4)(2.09)^2 by 3 to get 151,354.665. As a result my answer was -38,981.25 which I found out was wrong. What did I do wrong?

Problem 15.
Given: g=9.81m/s^2.
A 2.22 kg ball is attached to a ceiling by a 1.39m long string. The
height of the room is 3.60m. What is the gravational potential energy associated with the ball relative to
a. the ceiling?
Note:Would you use mgh=PE and have m=2.22 g=9.81 and h=3.60?
c. a point at the same elevation as the ball?
Note: How would you do it?

 

[Doc Al]

For the first problem, your solution looks OK to me. You found the change in total KE; perhaps they wanted change in KE for the third car alone.

For the second problem, use PE = mgh, where h is measured from your reference point. Relative to the ceiling, h = - 1.39; relative to the height of the ball, h = 0.0.

 

[M98Ranger]

In order to calculate the decrease in kinetic energy during the collision, you need to first find the total initial kinetic energy of all three railroad cars before the collision. This can be calculated by using the formula KE = 0.5mv^2, where m is the mass and v is the velocity.

For the single car, the initial kinetic energy would be KE = 0.5(2.31*10^4)(3.59)^2 = 149,895.81 J.

For the two cars already joined together, the initial kinetic energy would be KE = 0.5(2*2.31*10^4)(1.34)^2 = 9,876.36 J.

Therefore, the total initial kinetic energy before the collision is 149,895.81 + 9,876.36 = 159,772.17 J.

After the collision, the three cars join together and have a final speed of 2.09 m/s. The final kinetic energy can be calculated using the same formula, and it would be KE = 0.5(3*2.31*10^4)(2.09)^2 = 151,354.67 J.

Therefore, the decrease in kinetic energy during the collision is 159,772.17 - 151,354.67 = 8,417.50 J.

As for the second problem, to calculate the gravitational potential energy of the ball relative to the ceiling, you would use the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.

So, the gravitational potential energy of the ball relative to the ceiling would be PE = (2.22)(9.81)(3.60) = 79.07 J.

To calculate the gravitational potential energy of the ball relative to a point at the same elevation, you would use the same formula but with a height of 0, since the ball is at the same elevation. So, the gravitational potential energy would be PE = (2.22)(9.81)(0) = 0 J.

I hope this explanation helps clarify any confusion. It is important to carefully consider the equations and units when solving physics problems.