It is well known that bullets and other missiles fired at Superman simply bounce off his chest. Suppose that a gangster sprays Superman's chest with 8 g bullets at the rate of 110 bullets/min, the speed of each bullet being 550 m/s. Suppose too that the bullets rebound straight back with no change in speed. What is the magnitude of the average force on Superman's chest from the stream of bullets?
Δt=1min/110=60/110=0.55 s
FΔt=Δp= mΔv= m[v-(-v)] =2mv
F=2mv/Δt =2•0.008•550/0.55 =16 N
Well, if we're talking about bullets bouncing off Superman's chest, we might as well make Superman the lead singer of a bullet-ridden heavy metal band! 🤘
But, let's get serious for a moment. To find the magnitude of the average force on Superman's chest, we need to calculate the change in momentum for each bullet and then sum them up.
The change in momentum of each bullet can be calculated using the formula: Δp = 2m * v, where Δp is the change in momentum, m is the mass of the bullet, and v is the velocity.
Since we know the velocity (550 m/s) and the rate of bullets (110 bullets/min), we can find the mass of each bullet. One bullet is sprayed every 0.545 seconds (1 minute = 60 seconds), so the mass of each bullet is m = Δt * rate, where Δt is the time interval for each bullet.
Using the formula for force F = Δp/Δt, we can find the average force on Superman's chest. Since the time interval for each bullet is the same as the time interval between them (Δt), we can rewrite the formula as F = (2m * v) / Δt.
Substituting the values, we get:
F = (2 * m * v) / Δt
F = (2 * (Δt * rate) * v) / Δt
F = 2 * rate * v
Now we can calculate it:
F = 2 * 110 bullets/min * 550 m/s
F = 121,000 N
So, the magnitude of the average force on Superman's chest from the stream of bullets would be 121,000 Newtons. That's quite a force, but luckily for Supes, he can handle it!
To find the magnitude of the average force on Superman's chest, we need to calculate the change in momentum of the bullets that bounce off.
1. Calculate the mass of each bullet:
Mass = 8 g = 0.008 kg
2. Calculate the change in momentum per bullet:
Initial momentum = mass x initial velocity
Final momentum = mass x final velocity (since the bullets rebound with no change in speed)
Change in momentum = Final momentum - Initial momentum
Δp = (mass x final velocity) - (mass x initial velocity)
= mass x (final velocity - initial velocity)
= 0.008 kg x (550 m/s - (-550 m/s))
= 0.008 kg x (1100 m/s)
= 8.8 kg·m/s
3. Calculate the total change in momentum per minute:
Total change in momentum = Δp x number of bullets per minute
= 8.8 kg·m/s x 110 bullets/min
= 968 kg·m/s/min
4. Calculate the average force on Superman's chest:
Average force = Total change in momentum / Time interval
Since the time interval is not given, we cannot calculate the average force without that information.
To find the magnitude of the average force on Superman's chest from the stream of bullets, we can use the principle of momentum.
The momentum of an object is given by the product of its mass and velocity. The change in momentum of an object is equal to the force exerted on it multiplied by the time interval during which the force is applied. In this case, since the bullets rebound straight back with no change in speed, the change in momentum experienced by each bullet is two times its momentum.
First, let's calculate the momentum of each bullet:
Momentum = mass x velocity
Given:
Mass of each bullet = 8 g = 0.008 kg
Speed of each bullet, v = 550 m/s
Momentum of each bullet = (0.008 kg) x (550 m/s)
Momentum of each bullet = 4.4 kg·m/s
Since the bullets rebound straight back, the change in momentum experienced by each bullet is two times its momentum. Therefore, the change in momentum of each bullet is:
Change in momentum = 2 x Momentum of each bullet
Change in momentum = 2 x 4.4 kg·m/s
Change in momentum = 8.8 kg·m/s
Now, let's calculate the rate at which the bullets are being fired:
Rate of firing = 110 bullets/min
To find the average force, we need to calculate the time interval during which the force is applied.
Time interval = 1 minute = 60 seconds
Now, let's find the total change in momentum during 1 minute:
Change in momentum per bullet = 8.8 kg·m/s
Number of bullets fired per minute = 110 bullets/min
Total change in momentum = Change in momentum per bullet x Number of bullets fired per minute
Total change in momentum = 8.8 kg·m/s x 110 bullets/min
To find the average force, we divide the change in momentum by the time interval:
Average Force = Total change in momentum / Time interval
Average Force = (8.8 kg·m/s x 110 bullets/min) / 60 seconds
Calculating the average force:
Average Force = (8.8 kg·m/s x 110 bullets/min) / 60 seconds
Average Force = 16.06 kg·m/s²
Hence, the magnitude of the average force on Superman's chest from the stream of bullets is approximately 16.06 newtons.