We commonly see Superman being shot and bullets bounce off of him. Suppose Mr. Bad shoots Superman with 4.00 kg bullets at a rate of 100 bullets/min for 9.00 s. If the speed of each bullet is 480.00 m/s and rebounds straight back with no change in speed, calculate the magnitude of the average force experienced by Superman due to all the bullets.
To calculate the magnitude of the average force experienced by Superman due to all the bullets, we can use Newton's second law of motion, which states that force (F) is equal to the rate of change of momentum (p) over time (t).
The momentum of an object is given by the product of its mass (m) and velocity (v), so we can calculate the momentum of each bullet as the product of its mass and velocity.
The total momentum of the bullets hitting Superman is the sum of the momentum of each individual bullet, since momentum is a vector quantity.
The magnitude of the average force is then calculated by dividing the total change in momentum by the time over which the change occurs.
Let's perform the calculations:
1. Calculate the momentum of each bullet:
- mass of each bullet (m) = 4.00 kg
- velocity of each bullet (v) = 480.00 m/s
- momentum of each bullet (p) = m * v
2. Calculate the total momentum:
- Since bullets rebound straight back with no change in speed, the total momentum before and after the collision is zero.
3. Calculate the rate of change of momentum:
- rate of change of momentum = (Change in momentum) / (Time)
- Since the total momentum is zero, the average force is also zero.
Therefore, the magnitude of the average force experienced by Superman due to all the bullets is zero.
To calculate the magnitude of the average force experienced by Superman due to all the bullets, we can use Newton's second law of motion, which states that force is equal to the rate of change of momentum. Momentum is the product of mass and velocity.
First, we need to calculate the momentum of a single bullet. The momentum formula is:
p = m * v
where p is momentum, m is mass, and v is velocity.
Given that the mass of each bullet (m) is 4.00 kg and the velocity (v) is 480.00 m/s, we can calculate the momentum (p) for a single bullet as:
p = 4.00 kg * 480.00 m/s
Next, we need to find the rate of change of momentum, which is the momentum imparted to Superman by all the bullets. Since Mr. Bad is shooting at a rate of 100 bullets/min for 9.00 s, we first need to calculate the total number of bullets:
total number of bullets = rate of shooting * time
total number of bullets = (100 bullets/min) * (9.00 s)
Now, we can calculate the total momentum imparted to Superman:
total momentum = momentum per bullet * total number of bullets
total momentum = p * total number of bullets
Finally, to find the magnitude of the average force, we can divide the total change in momentum by the total time over which the bullets were shot, using the formula:
force = change in momentum / time
force = total momentum / time
Plugging in the values, we can calculate the magnitude of the average force experienced by Superman due to all the bullets.