A rifle fires a(n) 3 g bullet with a muzzle
velocity of 370 m/s into a block of wood. The
bullet comes to rest after it has made a(n)
17 cm deep hole in the wood.
v
a
What is the magnitude of the average frictional force slowed the bullet?
Answer in units of N
To find the magnitude of the average frictional force that slowed the bullet, we can use the concept of work done. The work done on an object can be calculated using the formula:
Work = Force x Distance
In this case, the work done on the bullet by the frictional force is equal to the change in its kinetic energy. The initial kinetic energy of the bullet can be calculated using the formula:
Initial Kinetic Energy = (1/2) x (Mass) x (Initial Velocity)^2
And the final kinetic energy of the bullet is zero since it comes to rest. Therefore, the work done by the frictional force is equal to the initial kinetic energy of the bullet.
Now, let's plug in the given values into the formulas:
Mass of the bullet (m) = 3 g = 0.003 kg
Initial velocity (v) = 370 m/s
Distance traveled (d) = 17 cm = 0.17 m
Initial Kinetic Energy = (1/2) x (0.003) x (370^2)
Now we can calculate the work done:
Work = Initial Kinetic Energy = (1/2) x (0.003) x (370^2)
Finally, we can convert the work done into the magnitude of the frictional force by dividing it by the distance traveled:
Frictional Force = Work / Distance = [(1/2) x (0.003) x (370^2)] / 0.17
Calculating this value gives us the magnitude of the average frictional force that slowed the bullet.
To find the magnitude of the average frictional force that slowed the bullet, we can make use of the principles of conservation of energy.
First, let's determine the initial kinetic energy (KE_initial) of the bullet. The formula for kinetic energy is:
KE = (1/2) * mass * velocity^2
Given:
Mass of the bullet = 3 g = 0.003 kg
Muzzle velocity = 370 m/s
KE_initial = (1/2) * 0.003 kg * (370 m/s)^2
KE_initial = 0.003 * (1/2) * 370^2
Next, let's determine the final kinetic energy (KE_final) of the bullet when it comes to rest. As the bullet comes to rest, all of its initial kinetic energy is converted into work done by friction.
The work done by friction can be calculated using the formula:
Work = Force * Distance
Given:
Depth of the hole in the wood = 17 cm = 0.17 m (since work is done against the friction over the distance equal to the depth of the hole)
Since the work done by friction is equal to the change in kinetic energy of the bullet, we can write:
Force * Distance = KE_initial - KE_final
Since the bullet comes to rest, KE_final = 0.
Force * 0.17 = KE_initial - 0
Force = KE_initial / 0.17
Finally, substitute the value of KE_initial to find the magnitude of the average frictional force that slowed the bullet:
Force = 0.003 * (1/2) * 370^2 / 0.17
Calculating this expression will provide you with the magnitude of the average frictional force in units of Newtons (N).