A 7.80-g bullet moving at 520 m/s penetrates a tree trunk to a depth of 4.60 cm.
(a) Use work and energy considerations to find the average frictional force that stops the bullet.
N
(b) Assuming the frictional force is constant, determine how much time elapses between the moment the bullet enters the tree and the moment it stops moving.
s
(a) (Avg. Force) x (penetration distance) = Initial kinetic energy
Fav = (M/2)Vo^2/(0.046 m)
= ___ Newtons
(b) (Penetration distance)/(average speed) = 4.60*10^-2 m/260 m/s
= 1.77*10^-4 s
69^2=5
To find the average frictional force that stops the bullet, we can use work and energy considerations. The work done by the frictional force is equal to the change in kinetic energy of the bullet.
(a) First, we need to calculate the initial kinetic energy of the bullet.
The formula for kinetic energy is:
K.E = (1/2) * mass * velocity^2
Given:
Mass of the bullet (m) = 7.80 g = 0.00780 kg
Initial velocity (v) = 520 m/s
Substituting the values into the formula:
K.E = (1/2) * 0.00780 kg * (520 m/s)^2
Calculating the value, we get:
K.E = 0.00780 kg * 270,400 m^2/s^2
= 2,111.2 J
The work done by the frictional force is equal to the change in kinetic energy:
Work = -ΔK.E
Since the bullet comes to a stop, the change in kinetic energy is equal to the initial kinetic energy (since the final kinetic energy is 0):
Work = -2,111.2 J
Now, let's calculate the work done by friction using the equation:
Work = Frictional force * distance
Given:
Distance (d) = 4.60 cm = 0.046 m (converted to SI unit)
Substituting the values into the equation:
-2,111.2 J = Frictional force * 0.046 m
Rearranging the equation to solve for the frictional force:
Frictional force = -2,111.2 J / 0.046 m
Calculating the value, we get:
Frictional force = -45,877.4 N (Note: the negative sign indicates that the force is opposite to the motion of the bullet)
Therefore, the average frictional force that stops the bullet is approximately 45,877.4 N.
(b) To determine the time it takes for the bullet to stop, we can use the equation:
Work = Force * Distance
Given:
Force (Frictional force) = 45,877.4 N
Distance (d) = 4.60 cm = 0.046 m (converted to SI unit)
Substituting the values into the equation:
Work = 45,877.4 N * 0.046 m
Simplifying the equation, we have:
Work = 2,109.3 J
The work done by the frictional force is also equal to the change in kinetic energy:
Work = -ΔK.E
Given:
Change in kinetic energy (ΔK.E) = 2,111.2 J
Rearranging the equation to solve for the time (t):
2,109.3 J = -2,111.2 J * t
Simplifying the equation, we get:
t = 2,109.3 J / (-2,111.2 J)
Calculating the value, we get:
t ≈ -0.9991 s
Therefore, the time it takes for the bullet to stop (assuming constant frictional force) is approximately 0.9991 seconds.