Question

A 7.80 g bullet has a speed of 530 m/s when it hits a target, causing the target to move 4.60 cm in the direction of the bullet's velocity before stopping. (a) Use work and energy considerations to find the average force (in N) that stops the bullet.

Answer 1

The average force that stops the bullet is found using the work-energy principle, equating the kinetic energy of the bullet to the work done by the force over the distance the target moves. The kinetic energy of the bullet is given as KE = (1/2)mv², and the work is Work = Fd. Solving for F gives an average force of 23667 N.

Step-by-step explanation:

To find the average force that stops the bullet, we can use the work-energy principle. The work done by the force to stop the bullet is equal to the change in the bullet's kinetic energy.

The kinetic energy (KE) of the bullet when it hits the target can be calculated using the formula:

KE = (1/2)mv²

where m is the mass of the bullet and v is its velocity. Plugging in the values:

KE = (1/2)(7.80 g)(530 m/s)²

Note that the mass should be converted to kilograms:

KE = (1/2)(0.00780 kg)(530 m/s)² = 1088.67 J

Since the bullet comes to rest, all of this energy is used to do work against the average force (F), which can be expressed as:

Work = Fd

where d is the distance the target moves. The distance needs to be in meters:

d = 4.60 cm = 0.0460 m

Equating the work done to the bullet's initial kinetic energy:

1088.67 J = F(0.0460 m)

Now, solve for F:

F = 1088.67 J / 0.0460 m = 23667 N

Therefore, the average force that stops the bullet is 23667 N.