Dynamic

EAS 215, Spring 2021 Assignment #9

1. For each open system shown below, what would be the total force, F, required to hold it stationary?

a.

b.

F !̇#$% = 3()/+ ,#$% = 20!/+

F !̇#$% = 3()/+ ,#$% = 20!/+

!̇/0 = 3()/+ ,/0 = 10!/+

c.

d.

F!̇#$ = 3'(/* +#$ = 10!/*

!̇./0 = 1.5'(/* +./0 = 20!/*

!̇./0 = 1.5'(/* +./0 = 20!/* 60°

60°

F!̇#$ = 3'(/* +#$ = 10!/*

!̇./0 = 1.5'(/* +./0 = 20!/*

!̇./0 = 1.5'(/* +./0 = 20!/*60°

60°

More Open Systems

2. A 5th Grade student made a rocket sled for a science fair. A bottle with pressurized

water and air was attached to a sled. The sled was propelled forward as water was ejected from the back. 𝜇" = 0.2 was the coefficient of friction between the sled and the ground. What was the acceleration of the sled at the moment shown below?

3. A toy rocket has two exhausts, each angled 30° from the axis of the rocket. At a particular moment the rocket has a mass of 1.5 kg and each exhaust has a mass flow of 0.5 kg/s and a speed of 25 m/s relative to the rocket. What is the acceleration of the rocket at that moment?

⛸ ⛸

g

S

!" = 0.5 (/* (̇, = 2 .//*

!,/"= 8 (/* (" = 10 ./

23 = 0.2

!"= 1.5 kg

30°30° !̇'() = 0.5 .//1 2'()/" = 25 !/1

!̇'() = 0.5 .//1 2'()/" = 25 !/1

g

4. A fire boat is floating on a still lake. The fire boat has two water cannons. One ejects water at 20 kg/s and 10 m/s at an angle 45° above horizontal. The other ejects water out of the opposite end of the boat at 16 kg/s and 10 m/s. The water cannons are fed by water that enters vertically through the bottom of the boat. At what angle, 𝜃+, should the second cannon be aimed so that the boat will not move in the water?

Fire Department

45°

$̇& = 20 kg/s *+,-&// = 10 m/s

23 = ?

$̇5 = 16 kg/s *+,-5// = 10 m/s

$̇78

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