   Chapter 5, Problem 15P

Chapter
Section
Textbook Problem

A 7.80-g bullet moving at 575 m/s penetrates a tree trunk to a depth of 5.50 cm. (a) Use work and energy considerations to find the average frictional force that stops the bullet. (b) Assuming the frictional force is constant, determine how much time elapses between the moment the ballet enters the tree and the moment it stops moving.

(a)

To determine
The average frictional force that stops the bullet.

Explanation

Given Info:

The mass of bullet is 7.80g .

The speed of bullet is 575m/s .

The distance that the bullet penetrates into the tree truck is 5.50cm .

Since, the bullet is penetrating in to the tree truck; the one and only force that is acting on the bullet is the average frictional force. So,

Wnet=(favcosθ)d       (I)

• fav is the average resistance force
• d is the displacement vector
• θ is the angle between the force vector and the displacement vector

From the Work-Energy theorem, the net work done on an object is equal to the change in kinetic energy of the object. The displacement vector is opposite to the resistance force exerted by the tree truck. So, the angle θ is vi 180° .

The equation (I) is given by,

(favcosθ)d=KEfKEi

• KEf is the final kinetic energy
• KEi is the initial kinetic energy

Hence, on rearranging,

Formula to calculate the average force of resistance is,

fav=KEfKEi(cosθ)d

Since, the final velocity of bullet is zero

(b)

To determine
The time elapses between the moments the bullet enters the tree and the moment it stop moving.

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