Exercise 1: Factors and Least Common Multiples

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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

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