7.18-g bullet moving at 563 m/s penetrates a tree trunk to a depth of 5.1 cm. Find the average frictional force that stops the bullet.
To find the average frictional force that stops the bullet, we can use the concept of work.
First, let's convert the depth of penetration into meters, as the bullet velocity is given in meters per second. We know that 1 cm is equal to 0.01 m, so 5.1 cm is equal to 5.1 * 0.01 = 0.051 m.
Now, we need to determine the work done by the friction force to bring the bullet to a stop. The work done is equal to the negative change in kinetic energy. Using the equation:
Work = -Change in kinetic energy
The change in kinetic energy is given by:
Change in kinetic energy = (1/2) * mass * (final velocity)^2 - (1/2) * mass * (initial velocity)^2
Where mass is the mass of the bullet, and the initial and final velocities are given as:
Initial velocity = 563 m/s
Final velocity = 0 m/s (since the bullet comes to a stop)
To find the mass of the bullet, we need to use the equation:
Kinetic energy = (1/2) * mass * velocity^2
Where the kinetic energy is given by:
Kinetic energy = (1/2) * mass * (initial velocity)^2
Rearranging the equation, we can solve for mass:
Mass = (2 * Kinetic energy) / (initial velocity)^2
Now, let's substitute the given values into the equations:
Initial velocity = 563 m/s
Final velocity = 0 m/s
Kinetic energy = (1/2) * mass * (initial velocity)^2
Mass = (2 * Kinetic energy) / (initial velocity)^2
The negative work done by the friction force is equal to the change in kinetic energy, so:
Work = -Change in kinetic energy
Finally, we can calculate the average frictional force using the formula:
Average frictional force = Work / Distance
Where distance is the distance over which the braking force is applied, which in this case is equal to the depth of penetration.
By following these steps and substituting the given values into the equations, you'll be able to find the average frictional force that stops the bullet.