Ohmygoodness, I am not having a good time tonight.

"A 5.2kg block sliding at 9.4 m/s across a horizontal frictionless surface collides head on with a stationary 8.6kg block. The 5.20kg block rebounds at 1.80 m/s. How much kinetic energy is lost during this collision?"

My FBD just isn't working; after I calculate momentum and attempt a vector diagram, my work falls apart. I'm really starting to panic!

K1=initial kinetic energy

K2=kinetic energy after collision

K1 = (1/2)(5.2kg)(9.4m/s)^2
K2 = (1/2)(5.2kg)(1.80m/s)^2

kinetic energy lost is:
K1 - K2

Use conservation of momentum to compute the velocity of the block that was initially stationary. Make sure you get the directions right. They will go off in opposite directions.

Once you have all the final velocities, compute how much the total kinetic energy decreased after the collision.

Quidditch's answer assumes block 2 remains stationary. I do not think that is what they want to to assume.

Disregard my answer. I assumed that the stationary block was fixed. I don't think that is the case. DRWLS has the correct approach. He is very good.

I'm sorry to hear that you're having a tough time with this problem. Let me help you through it step by step.

First, let's analyze the situation:

We have two blocks: a 5.2 kg block sliding at 9.4 m/s and an 8.6 kg stationary block. They collide head-on and the 5.2 kg block rebounds at 1.80 m/s. We need to find how much kinetic energy is lost during this collision.

Here's how you can approach this problem:

1. Start by calculating the initial momentum of the two blocks before the collision. Momentum is the product of mass and velocity, given by p = m * v.

For the 5.2 kg block:
Initial momentum = mass * velocity = 5.2 kg * 9.4 m/s

For the 8.6 kg block:
Initial momentum = mass * velocity = 8.6 kg * 0 m/s (since it is stationary)

2. Next, determine the final momentum of the 5.2 kg block. Since it rebounds at 1.80 m/s, the direction of its velocity changes. Momentum is a vector, so its direction is important. In this case, we consider the final momentum to be negative since it moves in the opposite direction.

Final momentum = mass * velocity = 5.2 kg * (-1.80 m/s)

3. Now, calculate the change in momentum (Δp) for the 5.2 kg block. This is given by the final momentum minus the initial momentum.

Δp = Final momentum - Initial momentum

4. Finally, to find the kinetic energy lost during the collision, we can use the relationship between kinetic energy and change in momentum.

Kinetic energy lost = (1/2) * m * (v_initial^2 - v_final^2)

Where m is the mass of the block and v_initial and v_final are the initial and final velocities, respectively.

In this case, since there is no friction, the kinetic energy lost is equal to the change in the kinetic energy of the 5.2 kg block.

Kinetic energy lost = (1/2) * 5.2 kg * (9.4 m/s)^2 - (1/2) * 5.2 kg * (1.80 m/s)^2

Simplifying this expression will give you the solution.

I hope this explanation helps you understand the problem better. Don't panic, take your time, and follow the steps. If you have any further questions, feel free to ask!