A body of 8.10 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?
To determine the mass of the struck body, we can use the principle of conservation of linear momentum.
The formula for linear momentum is given by: p = m * v
Where:
p is the linear momentum,
m is the mass, and
v is the velocity.
Let's denote the initial mass of the first body as m1 and its initial velocity as v1.
Given:
m1 = 8.10 kg
v1 = initial velocity of the first body
v2 = one-fourth of the original velocity of the first body
According to the principle of conservation of linear momentum:
The initial momentum of the system before the collision is equal to the final momentum of the system after the collision.
Initial momentum = Final momentum
Initial momentum = m1 * v1
Final momentum = (m1 + m2) * v2
Since the second body is initially at rest, its initial velocity (v2) is zero.
Therefore, the equation becomes:
m1 * v1 = (m1 + m2) * v2
Since v2 is one-fourth of v1, we can substitute v2 with v1/4:
m1 * v1 = (m1 + m2) * v1/4
Simplifying the equation by canceling out v1 on both sides:
4 * m1 = m1 + m2
3 * m1 = m2
m2 = 3 * m1
Substituting the given value of m1 into the equation:
m2 = 3 * 8.10 kg = 24.30 kg
Therefore, the mass of the struck body is 24.30 kg.