2. A .12 kg ball is moving at 6 m/s when it is hit by a bat, causing it to reverse direction and have a speed of 14 m/s. What is the change in the magnitude of the momentum of the ball?
4. Lonnie pitches a baseball of mass .2 kg. The ball arrives at home plate with a speed of 40 m/s and is batted straight back to Lonnie with a return speed of 60 m/s. If the bat is in contact with the ball for .050 s, what is the impulse experienced by the ball?
2. Although the momentum changes by 0.12 kg * [6 -(-14)m/s]= 2.4 kg m/s, becasue the direction reverses, the MAGNITUDE of the momentum changes only by 0.12 kg*(14 - 6)m/s = 0.72 kg m/s
4. Compute the momentum change, taking into account the direction change. That will equal the impulse. Divide that by the time interval of contact to get the average force.
To calculate the change in the magnitude of momentum, we need to first calculate the initial momentum and the final momentum of the ball in both scenarios.
For question 2:
1. Calculate the initial momentum (p_initial) of the ball using the formula: p_initial = mass * velocity
p_initial = 0.12 kg * 6 m/s
2. Calculate the final momentum (p_final) of the ball using the same formula:
p_final = mass * velocity
p_final = 0.12 kg * 14 m/s
3. Calculate the change in the magnitude of momentum using the formula: Δp = p_final - p_initial
For question 4:
1. Calculate the initial momentum (p_initial) of the ball using the formula: p_initial = mass * velocity
p_initial = 0.2 kg * 40 m/s
2. Calculate the final momentum (p_final) of the ball using the same formula:
p_final = mass * velocity
p_final = 0.2 kg * (-60 m/s) (since the direction of the ball is reversed)
3. Calculate the change in the magnitude of momentum using the formula: Δp = p_final - p_initial
Hope this helps! Let me know if you have any further questions.
To find the change in the magnitude of momentum in both questions, we'll use the formula:
Change in momentum = (final momentum) - (initial momentum)
Let's solve each question step by step:
2. We are given:
- Mass of the ball (m) = 0.12 kg
- Initial velocity (v1) = 6 m/s
- Final velocity (v2) = -14 m/s (negative sign indicates reversal of direction)
To find the initial momentum (p1), we'll use the formula:
p1 = m * v1
p1 = 0.12 kg * 6 m/s
p1 = 0.72 kg·m/s
To find the final momentum (p2), we'll use the same formula but with the final velocity:
p2 = m * v2
p2 = 0.12 kg * (-14 m/s)
p2 = -1.68 kg·m/s
Now, we can calculate the change in momentum:
Change in momentum = p2 - p1
Change in momentum = -1.68 kg·m/s - 0.72 kg·m/s
Change in momentum = -2.4 kg·m/s
Therefore, the change in the magnitude of the momentum of the ball is 2.4 kg·m/s.
4. We are given:
- Mass of the ball (m) = 0.2 kg
- Initial velocity (v1) = 40 m/s
- Final velocity (v2) = -60 m/s (negative sign indicates reversal of direction)
- Time of contact (t) = 0.050 s
To find the initial momentum (p1), we'll use the formula:
p1 = m * v1
p1 = 0.2 kg * 40 m/s
p1 = 8 kg·m/s
To find the final momentum (p2), we'll use the same formula but with the final velocity:
p2 = m * v2
p2 = 0.2 kg * (-60 m/s)
p2 = -12 kg·m/s
Now, we can calculate the change in momentum:
Change in momentum = p2 - p1
Change in momentum = -12 kg·m/s - 8 kg·m/s
Change in momentum = -20 kg·m/s
However, to find impulse, we need to use the definition of impulse:
Impulse = Change in momentum / Time of contact
Impulse = (-20 kg·m/s) / (0.050 s)
Impulse = -400 N·s
Note: Impulse is a vector quantity, and its negative sign indicates a change in direction.