A 7.24 g bullet moving at 636 m/s penetrates a tree to a depth of 4.87 cm. Use energy considerations to find the average frictional force that stops the bullet. Answer in units of N
B) Assuming that the frictional force is constant how much time elapsed between the moment of the bullet entering the tree and moment it stopped? Answer is Seconds
A) Initial Kinetic Energy
= Work done to stop
= (Avg. Force)*(Distance, X)
F = (1/2)(0.00724)*(636)^2/0.0487 m)
= ___ N
B) (Avg speed)*time = Distance
Time = 0.0487 m/318 m/s
= 1.53*10^-4 s
To find the average frictional force that stops the bullet, we can use the principle of conservation of energy.
First, we need to determine the initial kinetic energy of the bullet. The equation for kinetic energy is given by:
KE = (1/2)mv^2
Where m is the mass of the bullet and v is its velocity. Plugging in the given values, we have:
KE = (1/2)(7.24 g)(636 m/s)^2
Next, we need to determine the work done by the frictional force in stopping the bullet. The work done by a force can be calculated using the equation:
Work = force x distance
In this case, the distance traveled is the depth to which the bullet penetrates the tree, which is given as 4.87 cm. We convert it to meters by dividing by 100:
distance = 4.87 cm / 100
Now, the work done by the frictional force is equal to the change in kinetic energy of the bullet:
Work = delta(KE)
Since the bullet comes to a stop, its final kinetic energy is zero. Therefore, the work done by the frictional force is equal to the initial kinetic energy:
Work = KE = (1/2)(7.24 g)(636 m/s)^2
Now, we can find the average frictional force by dividing the work done by the distance traveled:
Average frictional force = Work / distance
Finally, we need to convert the mass of the bullet from grams to kilograms to get the answer in the correct units of Newtons (N):
Average frictional force = Work / distance = [(1/2)(7.24 g)(636 m/s)^2] / [4.87 cm / 100] = [(1/2)(0.00724 kg)(636 m/s)^2] / [0.0487 m]
Now, we can calculate this value to find the average frictional force that stops the bullet.
For the second part of the question, assuming the frictional force being constant, we can use the equation of motion:
v = u + at
Where:
- v is the final velocity (0),
- u is the initial velocity (636 m/s),
- a is the acceleration (equal to the average frictional force divided by the mass of the bullet),
- t is the time.
Rearranging the equation, we have:
t = (v - u) / a
Now, we can substitute the given values to find the time elapsed between the moment the bullet enters the tree and the moment it stopped.