Question

A 1kg cart slams into a stationary 1kg cart at 2 m/s. The carts stick together and move forward at a speed of 1 m/sl. Determine whether kinetic energy was conserved in the collision. Use the law of conservation of energy to explain the collision

Answer 1

No, it is not conserved

Step-by-step explanation:

Let's calculate the total kinetic energy before the collision and compare it with the total kinetic energy after the collision.

The total kinetic energy before the collision is:

`K_i = K_1 + K_2 = (1)/(2)mv_1^2 + (1)/(2)mv_2^2=(1)/(2)(1 kg)(2 m/s)^2+(1)/(2)(1 kg)(0)^2=2 J`

where m1 = m2 = 1 kg are the masses of the two carts, v1=2 m/s is the speed of the first cart, and where v2=0 is the speed of the second cart, which is zero because it is stationary.

After the collision, the two carts stick together with same speed v=1 m/s; their total kinetic energy is

`K_f = (1)/(2)(m_1+m_2)v^2=(1)/(2)(1 kg+1kg)(1 m/s)^2=1 J`

So, we see that the kinetic energy was not conserved, because the initial kinetic energy was 2 J while the final kinetic energy is 1 J. This means that this is an inelastic collision, in which only the total momentum is conserved. This loss of kinetic energy does not violate the law of conservation of energy: in fact, the energy lost has simply been converted into another form of energy, such as heat, during the collision.