# A 270 caliber hunting rifle fires an 8.5 g bullet, which exits the gun barrel at a speed of 980 m/s.

What impulse does the burning gunpowder impart to the bullet?
If it takes 2 ms for the bullet to travel the length of the barrel, what is the average force on the bullet?

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## To find the impulse imparted to the bullet by the burning gunpowder, we can use the principle of impulse-momentum.

Impulse (J) is given by the equation:
J = m * Δv

Where:
m = mass of the bullet
Δv = change in velocity of the bullet

In this case, the mass of the bullet (m) is 8.5 g, which is equal to 0.0085 kg, and the change in velocity (Δv) is the final velocity of the bullet after it exits the barrel, which is 980 m/s.

So, the impulse imparted to the bullet by the burning gunpowder is:
J = 0.0085 kg * 980 m/s
J ≈ 8.33 N·s

To find the average force on the bullet, we can use the equation:
F = Δp / Δt

Where:
Δp = change in momentum of the bullet
Δt = time taken for the bullet to travel the length of the barrel

The momentum of the bullet (p) is given by the equation:
p = m * v

Where:
m = mass of the bullet
v = velocity of the bullet

In this case, the mass of the bullet (m) is still 0.0085 kg, and the velocity (v) is 980 m/s. Therefore, the momentum of the bullet is:
p = 0.0085 kg * 980 m/s
p ≈ 8.33 kg·m/s

Since the time taken (Δt) for the bullet to travel the length of the barrel is given as 2 ms, which is equal to 0.002 s, the change in momentum (Δp) is the final momentum of the bullet after it exits the barrel, which is 8.33 kg·m/s.

Therefore, the average force on the bullet is:
F = Δp / Δt
F = 8.33 kg·m/s / 0.002 s
F ≈ 4165 N

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## To find the impulse imparted to the bullet by the burning gunpowder, we can use the equation:

Impulse = Change in momentum

The momentum of an object is defined as the product of its mass and velocity. In this case, the mass of the bullet is given as 8.5 grams, which can be converted to kilograms by dividing by 1000 (since there are 1000 grams in a kilogram). So the mass of the bullet is 8.5 g / 1000 = 0.0085 kg. The velocity of the bullet is given as 980 m/s.

Therefore, the initial momentum of the bullet is:

Initial momentum = mass × velocity = 0.0085 kg × 980 m/s

To find the final momentum, we need to know the final velocity of the bullet once it leaves the gun barrel. However, the given information does not provide this value. We will assume that there is no external force acting on the bullet after it leaves the barrel, resulting in a negligible change in velocity. In other words, we assume the final velocity of the bullet is also 980 m/s.

Given that the change in velocity is zero (final velocity - initial velocity = 0), the impulse imparted to the bullet by the burning gunpowder is the same as the initial momentum:

Impulse = Initial momentum = 0.0085 kg × 980 m/s

To calculate the average force on the bullet, we can use the equation:

Impulse = Average force × time

Rearranging the equation, we have:

Average force = Impulse / Time

The time taken for the bullet to travel the length of the barrel is given as 2 milliseconds (ms), which can be converted to seconds by dividing by 1000. So the time is 2 ms / 1000 = 0.002 s.

Now, we can substitute the values into the equation:

Average force = Impulse / Time = (0.0085 kg × 980 m/s) / 0.002 s

By calculating this expression, we can find the average force exerted on the bullet by the burning gunpowder.

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## I just did the other one, same deal

average force = impulse/time

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## Wow!

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