A 2.0 kg cart slams into a stationary 1.0 kg cart at 2.0 m/s. The carts stick together and move forward at a speed of 1.5 m/s. Was kinetic energy conserved in the collision?
Generally in collisions, momentum is conserved but kinetic energy may not be. To find out if it was in this case, lets look at the total kinetic energy before and after the collision: Before, the 2.0kg cart had [tex] E_{init}= \frac{1}{2}(2.0kg)(2.0 \frac{m}{s})^{2} =4J[/tex] and the second cart had no kinetic energy since its velocity was zero. So the total was 4J. After the collision the total mass was the sum of the 2 carts, or 3kg. Then the final kinetic energy is: [tex] \frac{1}{2}(3kg)(1.5 \frac{m}{s})^2=3.375J [/tex] As you see, the energy was not conserved. Momentum is conserved in elastic collisions and the mathematical reason is that the equation is linear; p=mv. The squared term in the kinetic energy usually leads to an imbalance because the sum of squares is not equal to the squares of sums: [tex] A^{2} + B^{2} \neq (A+B)^2[/tex] Physically, the energy is usually lost to heat in the bodies after the collision.
