Abel flicks a 20g marble at a speed of 0.5 m/s. It has one dimensional collision with a 10g bouncy ball, that was initially at rest. After they collide, the bouncy balls speed is 0.5 m/s. What is the marbles post-collision speed? Show whether or not any kinetic energy lost during the collision.
To find the marble's post-collision speed, we can use the principles of conservation of momentum and kinetic energy.
1. Begin by determining the initial momentum of the marble and the bouncy ball before the collision.
The momentum of an object is calculated by multiplying its mass by its velocity.
Marble's momentum (p1) = mass of the marble (m1) × velocity of the marble (v1) = 20 g × 0.5 m/s
Bouncy ball's momentum (p2) = mass of the bouncy ball (m2) × velocity of the bouncy ball (v2) = 10 g × 0 m/s (since it was initially at rest)
2. Apply the principle of conservation of momentum.
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
p1 + p2 = p1' + p2'
(20 g × 0.5 m/s) + (10 g × 0 m/s) = 20 g × v1' + 10 g × v2'
3. Combine the masses and solve for the marble's post-collision speed.
As mentioned before, the bouncy ball's speed after the collision is given as 0.5 m/s.
Substitute the known values into the equation and solve for v1' (the marble's post-collision speed):
(20 g × 0.5 m/s) + (10 g × 0 m/s) = (20 g × v1') + (10 g × 0.5 m/s)
(10 g × 0.5 m/s) = (20 g × v1') + (10 g × 0.5 m/s)
5 g m/s = (20 g × v1')
5 g m/s / 20 g = v1'
v1' = 0.25 m/s
Therefore, the marble's post-collision speed is 0.25 m/s.
To determine whether any kinetic energy was lost during the collision, we compare the initial kinetic energy (KE) with the final kinetic energy.
The kinetic energy of an object is calculated using the equation KE = 0.5 × mass × velocity^2.
For the marble:
Initial KE (KE1) = 0.5 × 20 g × (0.5 m/s)^2
Final KE (KE1') = 0.5 × 20 g × (0.25 m/s)^2
For the bouncy ball:
Initial KE (KE2) = 0.5 × 10 g × (0 m/s)^2 (since it was initially at rest)
Final KE (KE2') = 0.5 × 10 g × (0.5 m/s)^2
By comparing the initial and final kinetic energies, we can determine if there was any change or loss in kinetic energy during the collision.
To find the kinetic energies, simply calculate the expressions above using the given masses and velocities.