2 balls of clay , the first of mass 0.5kg,the other of mass 0.75kg approach each other ,each travels with a velocity of 0.5m\s,after the collision they stick together,what is the total energy after collision .Obtain the coefficient of restitution.
To determine the total energy after the collision, we need to calculate the initial kinetic energy and the final kinetic energy.
1. Calculate the initial kinetic energy:
The initial kinetic energy is given by the formula: KE = 0.5 * mass * velocity^2.
For the first ball:
Mass (m1) = 0.5 kg
Velocity (v1) = 0.5 m/s
Initial Kinetic Energy (KE1) = 0.5 * 0.5 * (0.5)^2 = 0.0625 Joules
For the second ball:
Mass (m2) = 0.75 kg
Velocity (v2) = -0.5 m/s (since they approach each other, their velocities have opposite signs)
Initial Kinetic Energy (KE2) = 0.5 * 0.75 * (-0.5)^2 = 0.09375 Joules
2. Calculate the final kinetic energy:
After the collision, the two balls stick together, so they become one object with a combined mass.
Combined mass (M) = m1 + m2 = 0.5 kg + 0.75 kg = 1.25 kg
Final velocity (vf) = ??? (This is what we need to find)
To calculate the final velocity, we can use the law of conservation of momentum:
Initial momentum (p1+2) = m1 * v1 + m2 * v2
Final momentum (p') = M * vf
According to the law of conservation of momentum, initial momentum should be equal to the final momentum: p1+2 = p'
m1 * v1 + m2 * v2 = M * vf
(0.5 kg * 0.5 m/s) + (0.75 kg * -0.5 m/s) = 1.25 kg * vf
0.25 kg m/s - 0.375 kg m/s = 1.25 kg * vf
-0.125 kg m/s = 1.25 kg * vf
Solving for vf:
vf = -0.125 kg m/s / 1.25 kg
vf = -0.1 m/s
Now we can calculate the final kinetic energy:
Final Kinetic Energy (KE') = 0.5 * M * vf^2
KE' = 0.5 * 1.25 kg * (-0.1 m/s)^2
KE' = 0.0625 Joules
3. Calculate the total energy after the collision:
The total energy after the collision is the sum of the final kinetic energy and any potential energy present.
Given the problem statement, it is assumed no potential energy is involved. Therefore, the total energy after the collision is equal to the final kinetic energy:
Total Energy after collision = KE' = 0.0625 Joules
4. Obtain the coefficient of restitution:
The coefficient of restitution (e) is defined as the ratio of relative velocity after the collision to the relative velocity before the collision.
Relative velocity before the collision = v2 - v1 = -0.5 m/s - 0.5 m/s = -1 m/s
Relative velocity after the collision = vf - v1 = -0.1 m/s - 0.5 m/s = -0.6 m/s
Coefficient of restitution (e) = relative velocity after collision / relative velocity before collision
e = -0.6 m/s / -1 m/s
e = 0.6
Therefore, the coefficient of restitution for this collision is 0.6.