A body of 5.10 kg mass makes an elastic collision with another body at rest and continues to move in the original direction, but with one-fourth of its original speed. What is the mass (in kilograms) of the struck body?
Assuming a perfectly elastic collision, KEi=KEf
ive tried solving this many ways and i keep ending up with 2 equations and 3 unknowns.
To solve this problem, you need to use the principles of conservation of momentum and kinetic energy.
Let's denote the mass of the body at rest as M, and the mass of the moving body as m. After the collision, the moving body continues to move in the same direction, but with one-fourth of its original speed.
1. Conservation of momentum:
Before the collision:
Initial momentum = m * Vi (where Vi is the initial velocity of the moving body). Since the other body is at rest, its momentum is zero.
After the collision:
Final momentum = m * Vf (where Vf is the final velocity of the moving body). The other body, which was at rest, acquires velocity after the collision. Let's denote the velocity of the other body as V.
According to the principle of conservation of momentum, the initial momentum equals the final momentum. So we have:
m * Vi = m * Vf + M * V
2. Conservation of kinetic energy:
Initially, the kinetic energy of the moving body is given by:
KE initial = (1/2) * m * Vi^2
After the collision, the kinetic energy of the moving body becomes:
KE final = (1/2) * m * (Vf/4)^2 = (1/32) * m * Vf^2
According to the principle of conservation of kinetic energy, the initial kinetic energy equals the final kinetic energy. Therefore:
(1/2) * m * Vi^2 = (1/32) * m * Vf^2
Now you have two equations: one from the conservation of momentum and another from the conservation of kinetic energy. By solving these equations simultaneously, you can determine the mass (M) of the struck body.
Although it seems like you have more unknowns than equations, it is possible to solve these equations using substitution or elimination methods. Start by rearranging the momentum equation to solve for Vf, then substitute this value into the kinetic energy equation.
By simplifying the resulting equation, you can find the value of the struck body's mass (M).