A ball of mass Ml = 0.250 kg and velocity V01 = +5.00 m/s (see Figure) collides head-on with a ball of mass
M2 = 0.800 kg that is initially at rest. No external forces act on the balls. a) What was the kinetic energy of the first ball before the collision; b) If the collision is completely inelastic, what are the velocities of the balls after collision?
a) Can you calculate (1/2)M1*Vo1^2?
b) by "completely inelastic" I assume you mean that they stick together and momentum ios conseved.
Write and solve the momentum conservation equation to get the final velocity (the same for both masses).
To answer these questions, we can use the principle of conservation of momentum and energy.
a) The kinetic energy of the first ball before the collision is given by the equation:
Kinetic energy = (1/2) * mass * velocity^2
Given that the mass of the first ball is Ml = 0.250 kg and the velocity is V01 = +5.00 m/s, we can calculate the kinetic energy:
Kinetic energy = (1/2) * 0.250 kg * (5.00 m/s)^2
Kinetic energy = 0.250 kg * 12.50 m^2/s^2
Kinetic energy = 3.125 J
So, the kinetic energy of the first ball before the collision is 3.125 Joules.
b) In a completely inelastic collision, the two balls stick together after the collision and move with a common velocity.
Using the conservation of momentum, we can write:
Initial momentum = Final momentum
Momentum of the first ball before the collision = Momentum of the system after collision
Ml * V01 = (Ml + M2) * Vf
Substituting the known values:
0.250 kg * 5.00 m/s = (0.250 kg + 0.800 kg) * Vf
1.25 kg*m/s = 1.05 kg * Vf
Solving for Vf, we get:
Vf = 1.25 kg*m/s / 1.05 kg
Vf ≈ 1.19 m/s
So, after the completely inelastic collision, the common velocity of the two balls is approximately 1.19 m/s.
To solve this problem, we need to use the principle of conservation of momentum and the principle of conservation of kinetic energy.
a) The kinetic energy (KE) of the first ball before the collision can be calculated using the formula:
KE1 = (1/2) * M1 * V01^2
where M1 is the mass of the first ball and V01 is its velocity.
Substituting the given values, we have:
KE1 = (1/2) * 0.250 kg * (5.00 m/s)^2
KE1 = 1.25 J
Therefore, the kinetic energy of the first ball before the collision is 1.25 Joules.
b) In a completely inelastic collision, the two masses stick together after collision and move with a common velocity. Let's call this velocity Vf.
To find the common velocity after the collision, we can use the conservation of momentum:
M1 * V01 + M2 * 0 = (M1 + M2) * Vf
Substituting the given values, we have:
0.250 kg * 5.00 m/s + 0.800 kg * 0 = (0.250 kg + 0.800 kg) * Vf
1.25 kg·m/s = 1.05 kg * Vf
Vf = 1.25 kg·m/s / 1.05 kg
Vf ≈ 1.19 m/s
Therefore, the velocities of the balls after the collision in a completely inelastic collision are approximately 1.19 m/s for both balls.