A rifle bullet with a mass of 16.5 g traveling toward the right at 285 m/s strikes a large bag of sand and penetrates it to a depth of 22.6 cm. Determine the magnitude and direction of the friction force (assumed constant) that acts on the bullet.
initial momentum = .0165 * 285
change of momentum = -.0165*285
average speed during stop = 285/2
time to stop = .226/average speed during stop
Force = change in momentum / time to stop
To determine the magnitude and direction of the friction force acting on the bullet, we need to use the principles of Newton's laws of motion.
First, we need to calculate the initial kinetic energy (KE) of the bullet:
KE = 1/2 * mass * velocity^2
Substituting the given values:
mass = 16.5 g = 0.0165 kg
velocity = 285 m/s
KE = 1/2 * 0.0165 kg * (285 m/s)^2
KE = 263.47 J (joules)
Next, we need to determine the work done by the friction force (Wfriction) to bring the bullet to a stop. This work done is equal to the energy lost by the bullet as it penetrates the bag of sand.
Given that the bullet penetrates a depth of 22.6 cm (or 0.226 m) in the sand, we can calculate the work done using the equation:
Wfriction = force * distance
The force applied by the friction is opposing the motion of the bullet, so its direction is opposite to the bullet's direction. Therefore, we take the negative value for the distance.
Wfriction = - KE
Now, substituting the known values:
Wfriction = -263.47 J
The work done by friction can also be expressed as:
Wfriction = friction force * displacement
Assuming the friction force is constant and acts over the whole displacement, we can rearrange the equation:
friction force = Wfriction / displacement
We have the values for Wfriction and the displacement, so we can substitute them into the equation:
friction force = -263.47 J / (0.226 m)
friction force = -1165.61 N (Newtons)
The negative sign indicates that the friction force is acting in the opposite direction to the bullet's motion.
Therefore, the magnitude of the friction force acting on the bullet is approximately 1165.61 N, and its direction is opposite to the bullet's motion (toward the left).