1. Part (1 of 2) A 5.36 g bullet oving at 681.8 m/s penetrates a tree trunk to a depth of 3.79 cm. a) Use work and energy considerations to find the magnitude of the force that stops the
bullet. Answer in units of N.
and
2. Part (2 of 2) b) Assuming that the frictional force is constant, determine how much time elapses between the moment the bullet enters the tree and the moment the bullets stops moving. Answer in units of s.
THANK YOU!!!
To solve both parts of the problem, we will use the principles of work and energy.
1. Part (1 of 2): Finding the magnitude of the force that stops the bullet.
To find the force, we will use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
First, let's find the initial kinetic energy of the bullet. The formula for kinetic energy is:
Kinetic energy = 1/2 * mass * velocity^2
Given:
Mass of the bullet (m) = 5.36 g = 0.00536 kg
Initial velocity (v) = 681.8 m/s
Plugging these values into the formula:
Initial kinetic energy = 0.5 * 0.00536 kg * (681.8 m/s)^2
Now, let's find the work done by the force that stops the bullet over a distance of penetration (d). The work done is given by:
Work = Force * Distance
Given:
Penetration depth (d) = 3.79 cm = 0.0379 m
Plugging these values into the formula, we get:
Work = Force * 0.0379 m
Since the work done equals the change in kinetic energy, we can equate the two expressions:
Force * 0.0379 m = 0.5 * 0.00536 kg * (681.8 m/s)^2
Solving for the force, we have:
Force = (0.5 * 0.00536 kg * (681.8 m/s)^2) / 0.0379 m
Evaluating the above expression will give us the magnitude of the force that stops the bullet, in units of Newtons (N).
2. Part (2 of 2): Finding the time elapsed between entering the tree and stopping.
To find the time elapsed, we can use the relationship between force, mass, and acceleration. The equation is:
Force = mass * acceleration
In this case, the acceleration is the deceleration of the bullet due to the constant frictional force acting in the opposite direction of its motion.
Given:
Mass of the bullet (m) = 5.36 g = 0.00536 kg
Force (from Part 1) = [calculate the value from Part 1]
Plugging these values into the equation, we have:
[calculate the value from Part 1] = 0.00536 kg * acceleration
Solving for acceleration:
acceleration = [calculate the value from Part 1] / 0.00536 kg
Now, we can find the time elapsed using the equation of motion:
Final velocity (vf) = initial velocity (vi) + acceleration * time
Given:
Final velocity (vf) = 0 m/s (bullet stops moving)
Initial velocity (vi) = 681.8 m/s (given)
Acceleration (a) = [calculate the value from above]
Plugging these values into the equation, we get:
0 m/s = 681.8 m/s + [calculate the value from above] * time
Solving for time will give us the time elapsed between the bullet entering the tree and stopping, in units of seconds (s).