Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 7, Problem 24P

(a)

To determine

The speed of the basketball.

(a)

Expert Solution
Check Mark

Answer to Problem 24P

The speed of the bullet and baseball combination is 33m/s.

Explanation of Solution

Since after the collision, the bullet and baseball combination must have the same momentum as the bullet had just before it stuck the baseball.

Write the equation for law of conservation of momentum.

pf=pi (I)

Here, pi is the initial momentum of the bullet before collision and pf is the final momentum of the bullet and baseball combination after the collision.

Write the equation for the momentum of the bullet before the collision.

pi=mbulletvi (II)

Here, pi is the initial momentum of the bullet before collision, mbullet is the mass of the bullet, and vi is the initial velocity of the bullet.

Write the equation for the momentum of bullet and baseball combination after the collision.

pf=(mbullet+mbaseball)vf (III)

Here, pf is the final momentum of the bullet and baseball combination after the collision, mbaseball is the mass of the baseball, and vf is the final velocity of the bullet and baseball combination.

Conclusion:

Substitute equation (III) and (II) in equation (I) and solve for vf.

(mbullet+mbaseball)vf=mbulletvivf=mbulletvi(mbullet+mbaseball)

Substitute 0.030kg for mbullet, 200m/s for vi, and 0.15kg for mbaseball in above equation.

vf=(0.030kg)(200m/s)(0.030kg+0.15kg)=6kgm/s0.18kg=33.3m/s=33m/s

Therefore, speed of the bullet and baseball combination is 33m/s.

(b)

To determine

The average force of baseball and bullet rising.

(b)

Expert Solution
Check Mark

Answer to Problem 24P

The average force of the baseball and bullet combination is 0.93N acting downward.

Explanation of Solution

Write the equation for the conservation of energy.

Ki+Ui+W=Kf+Uf (IV)

Here, Ki is the initial kinetic energy of the system, Ui is the initial potential enegy of the system, Kf is the final kinetic energy of the system, Uf is the final potential enegy of the system and W is the work done by the air resistance on the bullet and baseball combination.

Write the equation for kinetic energy.

K=12mv2 (V)

Here, m is the mass of the bullet and baseball combination and v is the velocity of the baseball and bullet combination.

Write the equation for potential energy.

U=mgyf (VI)

Here, g is the gravitational acceleration and yf is the height of the baseball and bullet rises.

Write the equation for work done by air resistance.

W=FavgΔyf (VII)

Here, Favg is the average force of air resistance.

Conclusion:

Substitute 0 for Ui and 0 for Kf in equation (IV).

Ki+0+W=0+UfKi+W=Uf (VIII)

Substitute equation (V) and (VI) in equation (VII) to find W.

12mv2+W=mgyfW=mgyf12mv2=m(gyf12v2)

Substitute 0.030kg+0.15kg=0.18kg for m, 9.80m/s2 for g, 37m for yf, and 33.3m/s for v in above equation.

W=0.18kg((9.80m/s2)(37m)12(33.3m/s)2)=0.18kg(362.6m2/s2554.4m2/s2)=34.5J

Rearrange equation (VII) for average force.

Favg=WΔyf

Substitute 34.5J for W and 37m for Δyf,

Favg=34.5J37m=0.93N

Therefore, the average force of the baseball and bullet combination is 0.93N acting downward.

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Chapter 7 Solutions

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