a 4 kilogram ball moving at 8 meters per second to the right collides with a 1 kilogram ball at rest. After the collision, the 4 kilogram ball moves at 4.8 meters per second to the right. What is the velocity of the 1 kilogram ball?
Conservation of momentum: total momentum before = total momentum after
Momentum = mass x velocity
So before the collision:
4kg x 8m/s = 32
1kg x 0m/s = 0
32+0=32
Therefore after the collision
4kg x 4.8m/s = 19.2
1kg x βm/s = β
19.2 + β = 32
Therefore β = 12.8 m/s
To determine the velocity of the 1 kilogram ball after the collision, we can use the principle of conservation of momentum. This principle states that the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) of an object is given by the product of its mass (m) and its velocity (v): p = m * v.
Before the collision, the 4 kilogram ball has a momentum of (4 kg) * (8 m/s) = 32 kg·m/s to the right.
After the collision, the 4 kilogram ball has a momentum of (4 kg) * (4.8 m/s) = 19.2 kg·m/s to the right.
Using the principle of conservation of momentum, we can calculate the momentum of the 1 kilogram ball after the collision.
Total momentum before collision = Total momentum after collision
(4 kg) * (8 m/s) + (1 kg) * (0 m/s) = (4 kg) * (4.8 m/s) + (1 kg) * (v)
32 kg·m/s = 19.2 kg·m/s + v
v = 32 kg·m/s - 19.2 kg·m/s
v = 12.8 kg·m/s
Therefore, the velocity of the 1 kilogram ball after the collision is 12.8 meters per second to the right.
To determine the velocity of the 1 kilogram ball after the collision, we can apply the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of a system remains constant if no external forces act on it. In this case, the two balls are the system and there are no external forces involved.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v):
p = m * v
Before the collision, the total momentum of the system is equal to the sum of the momentum of the 4 kilogram ball and the momentum of the 1 kilogram ball, which can be expressed as:
(4 kg * 8 m/s) + (1 kg * 0 m/s)
After the collision, the total momentum of the system is equal to the sum of the momentum of the 4 kilogram ball (4 kg * 4.8 m/s) and the momentum of the 1 kilogram ball (1 kg * v_final).
According to the principle of conservation of momentum, the total momentum before and after the collision remains the same.
Therefore, we can set up the equation:
(4 kg * 8 m/s) + (1 kg * 0 m/s) = (4 kg * 4.8 m/s) + (1 kg * v_final)
Simplifying this equation, we get:
32 kg·m/s = 19.2 kg·m/s + v_final
Rearranging the equation and isolating v_final, we find:
v_final = 32 kg·m/s - 19.2 kg·m/s
v_final = 12.8 kg·m/s
Therefore, the velocity of the 1 kilogram ball after the collision is 12.8 meters per second.