Question

a bullet moving with a speed of 300 m/s penetrates the body 5.0 cm deep calculate the force exerted by the body on the bullet if the mass of the bullet is 10 g​

Answer 1

Answer:

-18,000 N

Explanation:

Force = (Change in momentum) / (Time taken)

First, let's calculate the initial momentum of the bullet. The momentum of an object is given by:

Momentum = Mass × Velocity

Given that the mass of the bullet is 10 g (which is equal to 0.01 kg) and the speed of the bullet is 300 m/s, the initial momentum of the bullet is:

Initial momentum = 0.01 kg × 300 m/s = 3 kg·m/s

Next, we need to calculate the final momentum of the bullet. Since the bullet penetrates the body, its final velocity will be zero. Therefore, the final momentum is:

Final momentum = Mass × Final velocity = 0.01 kg × 0 m/s = 0 kg·m/s

The change in momentum is the difference between the initial momentum and the final momentum:

Change in momentum = Final momentum - Initial momentum = 0 - 3 kg·m/s = -3 kg·m/s

Now, we need to calculate the time taken for the bullet to come to rest. We know that the distance penetrated by the bullet is 5.0 cm, which is equal to 0.05 m. Since we don't have information about the deceleration, we cannot directly calculate the time taken. However, we can use the information given to estimate the deceleration using the following equation:

Distance = (Initial velocity × Time) + (0.5 × Deceleration × Time^2)

Plugging in the values, we get:

0.05 m = (300 m/s × Time) + (0.5 × Deceleration × Time^2)

Since the bullet comes to rest, the final velocity is zero. Therefore, the equation becomes:

0.05 m = 300 m/s × Time

Solving for Time, we find:

Time = 0.05 m / 300 m/s = 0.0001667 s

Now we can calculate the force exerted by the body on the bullet using the equation:

Force = (Change in momentum) / (Time taken)

Force = (-3 kg·m/s) / (0.0001667 s) = -18,000 N

The negative sign indicates that the force is exerted in the opposite direction to the bullet's initial motion.