Question
A ball of mass 800g moving horizontally with a speed of 5 meter per second hit a vertical wall and rebound with the same speed. Calculate the impulse experienced
Answers
GPT-4o mini
To calculate the impulse experienced by the ball when it hits the wall and rebounds, we can use the following formula for impulse:
\[
\text{Impulse} = \Delta p = p_{final} - p_{initial}
\]
where \( p \) is the momentum, given by \( p = mv \).
### Step 1: Calculate Initial Momentum
The initial momentum of the ball can be calculated using its mass and initial speed. Given that the mass \( m = 800 \, \text{g} = 0.8 \, \text{kg} \) (converting grams to kilograms) and the initial speed \( v_{initial} = 5 \, \text{m/s} \):
\[
p_{initial} = m \cdot v_{initial} = 0.8 \, \text{kg} \cdot 5 \, \text{m/s} = 4 \, \text{kg m/s}
\]
### Step 2: Calculate Final Momentum
After hitting the wall, the ball rebounds with the same speed but in the opposite direction. Therefore, the final velocity \( v_{final} = -5 \, \text{m/s} \):
\[
p_{final} = m \cdot v_{final} = 0.8 \, \text{kg} \cdot (-5) \, \text{m/s} = -4 \, \text{kg m/s}
\]
### Step 3: Calculate the Change in Momentum
Now we can calculate the impulse (change in momentum):
\[
\Delta p = p_{final} - p_{initial} = -4 \, \text{kg m/s} - 4 \, \text{kg m/s} = -8 \, \text{kg m/s}
\]
### Step 4: Impulse
The impulse experienced by the ball is \( -8 \, \text{kg m/s} \). The negative sign indicates that the impulse direction is opposite to the initial direction of the ball.
Thus, the magnitude of the impulse is:
\[
\text{Impulse} = 8 \, \text{Ns}
\]
### Final Answer
The impulse experienced by the ball is \( 8 \, \text{Ns} \).
\[
\text{Impulse} = \Delta p = p_{final} - p_{initial}
\]
where \( p \) is the momentum, given by \( p = mv \).
### Step 1: Calculate Initial Momentum
The initial momentum of the ball can be calculated using its mass and initial speed. Given that the mass \( m = 800 \, \text{g} = 0.8 \, \text{kg} \) (converting grams to kilograms) and the initial speed \( v_{initial} = 5 \, \text{m/s} \):
\[
p_{initial} = m \cdot v_{initial} = 0.8 \, \text{kg} \cdot 5 \, \text{m/s} = 4 \, \text{kg m/s}
\]
### Step 2: Calculate Final Momentum
After hitting the wall, the ball rebounds with the same speed but in the opposite direction. Therefore, the final velocity \( v_{final} = -5 \, \text{m/s} \):
\[
p_{final} = m \cdot v_{final} = 0.8 \, \text{kg} \cdot (-5) \, \text{m/s} = -4 \, \text{kg m/s}
\]
### Step 3: Calculate the Change in Momentum
Now we can calculate the impulse (change in momentum):
\[
\Delta p = p_{final} - p_{initial} = -4 \, \text{kg m/s} - 4 \, \text{kg m/s} = -8 \, \text{kg m/s}
\]
### Step 4: Impulse
The impulse experienced by the ball is \( -8 \, \text{kg m/s} \). The negative sign indicates that the impulse direction is opposite to the initial direction of the ball.
Thus, the magnitude of the impulse is:
\[
\text{Impulse} = 8 \, \text{Ns}
\]
### Final Answer
The impulse experienced by the ball is \( 8 \, \text{Ns} \).