Momentum Head on Collision Cart Problem

[bleedblue1234]

Homework Statement

Two remote control cars with masses of 1.11 kilograms and 1.81 kilograms travel toward each other at speeds of 8.75 meters per second and 3.39 meters per second, respectively. The cars collide head-on, and the less massive car recoils with a speed of 2.99 meters per second. How much kinetic energy was lost in the collision?

Homework Equations

no idea

The Attempt at a Solution

I don't really understand how to start... I was thinking we could calculate the total momentum of the system then calculate the ideal final velocity of the less massive cart then calculate the difference?

Would you fine the total momentum of the system... thus (1.11 kg)(8.75 m)+(1.81 kg)(- 3.39m) = 3.5766 kg * m /s then divide that by 1.11 kg to find the ideal velocity of the smaller cart... or 3.22216ish m/s... then get the kinetic energy of that which will be 1/2(1.11)(3.2216)^2 = 5.762192 J , then find the kinetic energy of the kinetic energy of it actually, or 1/2(1.11)(2.99)^2 = 4.961755 then subtract 5.7621 - 4.9617 = .800 J ?

 

[XanziBar]

I think you're on the right track. Use conservation of momentum to find the velocity of the other cart after the collision. The total kinetic energy before the collision can be calculated using (1/2)*m*v^2 for each of the carts. If you do the same after, the kinetic energy will be less. So you're right, subtract.

 

[JDHalfrack]

Ultimately, we are trying to find \DeltaKE which is equal to KE_f - KE_i.

KE_f = KE_1,f + KE_2,f and KE_i = KE_1,i + KE_2,i

KE_f = \frac{1}{2}m₁v_1,f² + \frac{1}{2}m₂v_2,f² and KE_i = \frac{1}{2}m₁v_1,i² + \frac{1}{2}m₂v_2,i²

Therefore, \DeltaKE = \frac{1}{2}(m₁v_1,f² + m₂v_2,f² - m₁v_1,i² - m₂v_2,i²)

Of course, we don't know v_2,f, so we have to use conservation of momentum to find it.

Since the law of conservation of momentum tells us that p_i = p_f and we know p = mv, then it follows that m₁v_1,i + m₂v_2,i = m₁v_1,f + m₂v_2,f

Solving for v_2,f, we get v_2,f = ( m₁v_1,i + m₂v_2,i - m₁v_1,f ) / m₂

After solving for v_2,f, you can substitute that value into the \DeltaKE equation, and that should tell you the amount of KE lost.