A ball of mass 0.75kg moving horizontally at 5m/s strikes a vertical wall and rebounds with a speed of 2m/s.find (a)what is the impulse received by the ball?(b)calculate the coefficient of restitution(c)calculate the kinetic energy of the ball before and after collision.
been there, done that.
To answer these questions, we need to understand the concepts of impulse, coefficient of restitution, and kinetic energy. Let's go through each question step by step:
(a) What is the impulse received by the ball?
Impulse is defined as the change in momentum of an object. In this case, the momentum of the ball before the collision is given by the product of its mass (m) and velocity (v1), and the momentum after the collision is given by the product of its mass and velocity (v2).
The formula for impulse (J) is given as:
J = m * (v2 - v1)
Given:
Mass (m) = 0.75 kg
Initial velocity (v1) = 5 m/s
Final velocity (v2) = -2 m/s (since the ball rebounds in the opposite direction)
Now we can calculate the impulse:
J = 0.75 kg * (-2 m/s - 5 m/s)
J = 0.75 kg * (-7 m/s)
J = -5.25 kg·m/s
Therefore, the impulse received by the ball is -5.25 kg·m/s.
(b) Calculate the coefficient of restitution:
The coefficient of restitution (e) is a measure of the elasticity of a collision. It is defined as the ratio of the relative velocity of separation (v2 - v1) to the relative velocity of approach (u1 - u2). In a perfectly elastic collision, the coefficient of restitution is 1.
The formula for the coefficient of restitution is given as:
e = (v2 - v1) / (u1 - u2)
In this case, the relative velocity of approach (u1 - u2) is equal to the initial velocity (v1), and the relative velocity of separation (v2 - v1) is equal to the final velocity (v2).
Now we can calculate the coefficient of restitution:
e = (2 m/s - (-2 m/s)) / (5 m/s - 0 m/s)
e = 4 m/s / 5 m/s
e = 0.8
Therefore, the coefficient of restitution is 0.8.
(c) Calculate the kinetic energy of the ball before and after the collision:
The kinetic energy (KE) of an object is given by the formula:
KE = 0.5 * m * v^2
Before the collision, the kinetic energy is given by:
KE_before = 0.5 * 0.75 kg * (5 m/s)^2
After the collision, the kinetic energy is given by:
KE_after = 0.5 * 0.75 kg * (2 m/s)^2
Now we can calculate the kinetic energies:
KE_before = 0.5 * 0.75 kg * (25 m^2/s^2)
KE_before = 9.375 J
KE_after = 0.5 * 0.75 kg * (4 m^2/s^2)
KE_after = 3 J
Therefore, the kinetic energy of the ball before the collision is 9.375 J, and after the collision is 3 J.