A 25-kg bullet traveling shoots into a physics textbook that is 3.5 cm wide, and exits the textbook traveling 40 m/s. Poor defenseless textbook! (A) What was the magnitude of the average deceleration of the bullet while it was penetrating through the textbook? (B) What was the magnitude of the average resistive force exerted on the bullet while it was penetrating through the textbook?
you have final velocity, but not starting velocity. Cant be determined.
If you had starting velociy, you could have
avgforce*time=massllet(vi-vf)
and the time is distance/avg velocity
avgvelocity=(vf+vi)/2
so you have resistive force.
for acceleration, a=avgvorce/massbullet
There are other ways, but you need the initial velocity.
To solve this problem, we need to use the principles of Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration, F = m * a.
(A) To find the magnitude of the average deceleration (negative acceleration) experienced by the bullet, we need to determine the change in velocity and the time taken to achieve this change.
Given:
- Mass of the bullet (m) = 25 kg
- Initial velocity of the bullet (u) = 0 m/s
- Final velocity of the bullet (v) = 40 m/s
The change in velocity is given by Δv = v - u = 40 - 0 = 40 m/s.
Next, we need to calculate the time (t) taken for the bullet to decelerate and come to rest inside the textbook. We can use the equation of motion: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Since the bullet comes to rest (u = 0), we can rearrange the equation as follows: v = at, and solve for time (t).
t = v / a
Substituting the values, t = 40 / a.
Now, we can use kinematic equations to determine the average deceleration. The average acceleration is given by the formula: a = Δv / t.
Substituting the values: a = 40 / (40 / a) = a
Simplifying the equation: a^2 = 40.
Therefore, the magnitude of the average deceleration of the bullet while penetrating the textbook is sqrt(40) m/s².
(B) To find the magnitude of the average resistive force exerted on the bullet while penetrating the textbook, we can use Newton's second law, F = m * a.
Substituting the values, F = 25 kg * sqrt(40) m/s² = 5 * sqrt(10) N.
Hence, the magnitude of the average resistive force exerted on the bullet while penetrating the textbook is 5 * sqrt(10) Newtons.