PHYC380
Classical Mechanics
Name _______________
Date ________________
Exercise 9: Momentum and Impulse
1. A rocket of mass m traveling with speed v
0
along the x axis suddenly shoots out fuel equal to one-third its mass, perpendicular to the x axis (along the y axis) with speed 2 v
0
.
Express the final velocity of the rocket in i , j , k notation. p i
= mv
0
i p f
= 2/3 mv + 1/3 m 2 v
0 j p i
= p f v = 3/2 v
0 i − v
0
j
2. A golf ball of mass 0.045 kg is hit off the tee at a speed of 45 m/s. The golf club was in contact with the ball for 3.5x10
−3
sec. Find a) the impulse imparted to the golf ball and b) the average force exerted on the ball by the golf club.
One dimension a. J = Δp = p f
− p i
= (0.045)(45) − 0 = 2.02 kg-m/s in the forward direction b. F avg
= Δp/Δt = 2.02/3.5x10
−3
= 580 N
3. Rain is falling at the rate of 5.0 cm/hr and accumulates in a pan. If the raindrops hit at
8.0 m/s, estimate the force on the bottom of a 1.0-m
2
pan due to the impacting rain, which does not rebound. Water has a density of 1.0x10
3
kg/m
3
F avg
= Δ p
/Δ t
What is mass in one hour? m =
ρV
= (1x10
3
)(0.05)(1) = 50 kg p f
= mv f
= 50(0) p i
= mv i
= − 50(8.0) = − 400
Δ p = 0 − (−400) = 400 kg-m/s
Δ t = 1 hour = 3600 s
F avg
= Δ p
/Δ t = 400/3600 = 0.11 N