Answer:
final velocity of ball 1 (v2) is approximately 4.3 m/s
final velocity of ball 2 (v2') is approximately 8.6 m/s
average force on the first ball is 102 N.
average force on the second ball is also 102 N.
Step-by-step explanation:
Certainly! Here's the math behind the analysis:
Using the equation of motion to calculate the final velocity of ball 1 (v2):
v2 = (m1 * v1) / (m1 + m2)
= (0.28 kg * 8.6 m/s) / (0.28 kg + 0.28 kg)
≈ 4.3 m/s
Using the principle of conservation of momentum to calculate the velocity of ball 2 (v2'):
m1 * v1 + m2 * 0 = m1 * 0 + m2 * v2'
0.28 kg * 8.6 m/s = 0.28 kg * v2'
v2' = (0.28 kg * 8.6 m/s) / 0.28 kg
≈ 8.6 m/s
Therefore, the final velocity of ball 1 (v2) is approximately 4.3 m/s, and the final velocity of ball 2 (v2') is approximately 8.6 m/s in the opposite direction of ball 1's initial motion.
The average force on the first ball is equal to the average force on the second ball. This is because the two balls are identical and exert equal and opposite forces on each other during the collision.
To calculate the average force, we can use the following equation:
```
F = (∆p)/∆t
```
where
* F is the average force
* ∆p is the change in momentum
* ∆t is the time interval
The change in momentum for the first ball is equal to the momentum of the first ball before the collision minus the momentum of the first ball after the collision. The momentum of the first ball before the collision is equal to its mass times its velocity. The momentum of the first ball after the collision is zero, since the first ball comes to rest.
Therefore, the change in momentum for the first ball is:
```
∆p = m(v_1 - 0) = m(v_1)
```
The time interval is given as 250 μs.
Therefore, the average force on the first ball is:
```
F = (∆p)/∆t = m(v_1)/∆t
```
```
F = (0.28 kg)(8.6 m/s) / (250 μs) = 102 N
```
Therefore, the average force on the first ball is 102 N. The average force on the second ball is also 102 N.
A billiard ball hits another billiard ball.
The first billiard ball stops moving.
The second billiard ball starts moving.
The force that made the first billiard ball stop is called the average force.
The average force is the same on both billiard balls.
The average force is 102 N.
Two balls are rolling towards each other. They are the same size and weight.
The first ball hits the second ball with a speed of 8.6 meters per second.
After the collision, the first ball stops moving, and the second ball starts moving.
The collision happens very quickly, lasting only 250 microseconds (which is a very short time).
We want to find out how hard the balls hit each other.
We know that the first ball had a mass of 0.28 kilograms.
We also know that the first ball stopped completely, so its final speed is 0 meters per second.
Using a rule called the "conservation of momentum," we can figure out what happened.
Momentum is a word that means how hard something is moving.
The rule says that the total momentum before the collision should be the same as the total momentum after the collision.
We can find the momentum by multiplying the mass of an object by its speed.
The momentum before the collision is equal to the momentum after the collision.
Since the first ball stops, its momentum after the collision is 0.
The second ball moves with a speed of 8.6 meters per second after the collision.
To find the force, we use the formula: Force = Change in momentum ÷ Time.
The change in momentum for the first ball is its initial momentum (which is its mass times its speed) minus its final momentum (which is 0).
The change in momentum for the second ball is its final momentum (which is its mass times its speed) minus its initial momentum (which is the same as before the collision).
The time of the collision is very short, so it's represented as 250 microseconds (which is a tiny fraction of a second).
By plugging in the values, we can calculate the average force on each ball.
The average force on the first ball is non-zero, meaning it experiences some force.
The average force on the second ball is 0, meaning it doesn't experience any force.
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The average force on the first ball can be calculated using the formula `F = m * (v_f - v_i) / t`, where `F` is the average force, `m` is the mass of the ball, `v_f` is the final velocity of the ball, `v_i` is the initial velocity of the ball and `t` is the time duration of the collision.
Since the first ball comes to rest after the collision, its final velocity `v_f` is 0 m/s. Substituting the given values in the formula, we get:
`F = 0.28 kg * (0 m/s - 8.6 m/s) / 250e-6 s`
`= -9664 N`
The negative sign indicates that the force is in the opposite direction to the initial velocity of the first ball.
average force on the second ball is equal to that on the first ball but in the opposite direction. Therefore, the average force on the second ball is `9664 N`.