
Concept explainers
(a)
The acceleration of the bullet.
(a)

Answer to Problem 82P
The bullet has an acceleration of 3.20×104m/s2.
Explanation of Solution
Write the
v=v0+abΔt (I)
Here, v is the final velocity of the bullet, v0 is the initial velocity of the bullet, ab is the acceleration of the bullet and Δt is the time taken by the bullet to leave the barrel.
Rewrite equation (I) to obtain an equation for ab.
ab=v−v0Δt
Conclusion:
Substitute 320m/s for v, 0m/s for v0 and 0.01s for Δt.
ab=320m/s−0m/s0.01s=3.20×104m/s2
Therefore, the acceleration of the bullet is 3.20×104m/s2.
(b)
The force on the bullet.
(b)

Answer to Problem 82P
The force on the bullet is 96.0N.
Explanation of Solution
Write the equation for the force on the bullet using Newton’s second law.
Fb=mab
Here, Fb is the force on the bullet, m is the mass of the bullet and ab is the acceleration of the bullet.
Conclusion:
Substitute 3.00×10−3kg for m and 3.20×104m/s2 for ab.
Fb=(3.00×10−3kg)(3.20×104m/s2)=96.0N
Therefore, the force on the bullet is 96.0N.
(c)
The magnitude of force exerted on the gun.
(c)

Answer to Problem 82P
The magnitude of force exerted on the gun is 96.0N.
Explanation of Solution
According to
Fb=−Fr
Here, Fb is the force on the bullet and Fr is the reverse force exerted by the bullet on the gun.
Conclusion:
Substitute 96.0N for Fb.
Fr=−96.0N
Therefore, the magnitude of force exerted on the gun is 96.0N. The negative sign in the answer indicates that the reaction is in the opposite direction.
(d)
The acceleration experienced by the gun
(d)

Answer to Problem 82P
The gun experiences an acceleration of −18.5m/s2.
Explanation of Solution
Write the equation for the force on the gun using Newton’s second law.
Fr=Mar
Here, Fb is the force on the gun, M is the mass of the gun and ar is the acceleration of the gun.
Conclusion:
Substitute −96.0N for Fr and 5.20kg for M to solve for ar.
−96.0N=(5.20kg)arar=−96.0N5.20kg=−18.5m/s2
Therefore, the acceleration experienced by the gun is −18.5m/s2.
(e)
The ratio of mass m and M to that of the acceleration.
(e)

Answer to Problem 82P
The acceleration ration is the inverse mass ratio.
Explanation of Solution
Write the ratio for mass m to M and substitute the values.
Mm=5.20kg3.00×10−3kg=1.73×103 (II)
Write the ratio of the acceleration and substitute.
abar=3.20×104m/s2−18.5m/s2=−1.73×103 (III)
Conclusion:
From equation (II) and (III), the acceleration ration is the inverse ratio of the mass.
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Chapter 3 Solutions
College Physics, Volume 1
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