A 5.4 g bullet leaves the muzzle of a rifle with a speed of 334 m/s. What force (assumed constant) is exerted on the bullet while it is traveling down the 0.95 m long barrel of the rifle?

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To find the force exerted on the bullet while it is traveling down the barrel of the rifle, we can use the equation:

Force = mass × acceleration

First, we need to find the acceleration of the bullet. We can use the equation:

acceleration = (final velocity - initial velocity) / time

Since the bullet travels the entire length of the barrel in a negligible amount of time, we can use the equation:

acceleration = (final velocity - initial velocity) / time = (334 m/s - 0 m/s) / 0 s = 334 m/s / 0 s = infinity

The acceleration is infinite because the bullet reaches its final velocity in a negligible amount of time. Therefore, the force can be considered to be applied over a very brief period.

However, if we want to find the average force exerted on the bullet over its entire journey down the barrel, we can use the equation:

Force = mass × acceleration

The mass of the bullet is given as 5.4 g, which is equal to 0.0054 kg.

Force = 0.0054 kg × infinity

Since the acceleration is approaching infinity, the force is also infinite. However, in reality, the force that propels the bullet is not infinite but rather is exerted over a very short period of time. Therefore, the instantaneous force exerted on the bullet while it is traveling down the barrel cannot be accurately determined using the given information.

To find the force exerted on the bullet while it is traveling down the barrel of the rifle, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = m * a).

First, we need to find the acceleration of the bullet. We can use the formula for acceleration:

acceleration = change in velocity / time

Since the bullet starts from rest and reaches a velocity of 334 m/s, the change in velocity is 334 m/s. However, we don't have the time taken for the bullet to reach this velocity.

To find the time, we can use the formula for average velocity:

average velocity = (initial velocity + final velocity) / 2

Since the bullet starts from rest, the initial velocity is 0. The final velocity is 334 m/s. Plugging these values into the formula, we get:

average velocity = (0 + 334) / 2 = 167 m/s

Next, we can find the time taken by dividing the distance traveled by the average velocity:

time = distance / average velocity

The distance traveled is given as 0.95 m. Plugging in the values, we get:

time = 0.95 m / 167 m/s = 0.0057 s

Now that we have the time, we can find the acceleration:

acceleration = change in velocity / time = 334 m/s / 0.0057 s = 58596 m/s²

Lastly, we can find the force by multiplying the mass of the bullet by the acceleration:

force = mass * acceleration = 5.4 g * 58596 m/s²

To convert grams to kilograms, we divide by 1000:

force = (5.4 g / 1000) * 58596 m/s² = 0.0054 kg * 58596 m/s²

Now we can calculate the force:

force = 0.0054 kg * 58596 m/s² = 316 N

Therefore, the force exerted on the bullet while it is traveling down the barrel of the rifle is approximately 316 N.