Physics question below?

Question

A projectile (mass = 0.24 kg) is fired at and embeds itself in a target (mass = 2.61 kg). The target (with the projectile in it) flies off after being struck. What percentage of the projectile's incident kinetic energy does the target (with the projectile in it) carry off after being struck?

Answer 1

We can't use conservation of energy because this is an inelastic collision. Conservation of momentum does hold, so

m1*u1 + m2*u2 = (m1+m2)*v

u2 is zero. So

v = m1*u1/(m1+m2) = .24 kg*u1/2.85 kg = .084*u1

The projectile's incident kinetic energy
KEp = (1/2)*m1*u1^2 = 0.12*u1^2 joules
The final kinetic energy
KEf = (1/2)*(m1+m2)*v^2 = 1.42*(.084*u1)^2 = .0100*u1^2 joules.

Percentage = 100%*KEf/KEp

Answer 2

I would say 100%. There will be some small heating of the target and projectile upon impact which may radiate off as well as the energy expended in vibrating the surrounding medium (air) to produce sound of impact. These will be very small for small velocities of the projectile. Since you gave no velocities or angles of incidence no calculations of the momentum of the resulting target/projectile mass is possible.

Answer 3

Kinetic energy = 1/2 MV ^2

We assume no energy is lost so all of it is shared between the two masses. This is called the conservation of momentum.

If you sub in the values and give a velocity of 1, all you can state is that the new mass moves off at 0.3 i.e. approximately one third of the initial velocity.