Forces & Motion Standard 9 Examples
A sailor uses a rope and an old, squeaky pulley to raise a sail that weighs 140 N. He finds that he must do 180 J of work on the rope to raise the sail by 1 m. (He does 140 J of work on the sail.) What is the efficiency of the pulley?
Efficiency = (140 J)/(180 J) = 0.78 = 78%
Alice and Jim calculate that they must do 1800 J of work to push a piano up a ramp. However, because they must also overcome friction, they actually must do 2400 J of work. What is the efficiency of the ramp?
Efficiency = (1800 J)/(2400 J) = .75 = 75%
What is the kinetic energy of a 0.02 kg bullet that is traveling 300 m/s?
KE = ½(0.02 kg)(300 m/s)² = 900 J
Calculate the kinetic energy in joules of a 1,500 kg car that is moving at a speed of 12 m/s?
KE = ½(1500 kg)(12 m/s)² = 108,000 J or 1.08 x 10⁵ J
A student lifts a 12 N textbook 1.5 m in 1.5 s and carries the book 5 m across the room in 7 s. What is the power output of the student?
P = (12 N x 1.5 m)/1.5 s = 12 W
How much power is used when a 43 N force is exerted through a distance of 2.0 m over a time of 3.0 s?
P = (43 N x 2 m)/3 s = 28.7 W
Anna walks up the stairs on her way to class. She weighs 565 N, and the stairs go up 3.25 m vertically. If Anna climbs the stairs in 10.5 s, what is her power output?
P = (565 N x 3.25 m)/10.5 s = 175 W
Anna walks up the stairs on her way to class. She weighs 565 N, and the stairs go up 3.25 m vertically. If Anna climbs the stairs in 12.6 s, what is her power output?
P = (565 N x 3.25 m)/12.6 s = 146 W
While rowing across the lake during a race, John does 3960 J of work on the oars in 60.0 s. What is his power output in watts?
P = 3960 J/60 s = 66 W
Calculate the potential energy of a 1200 kg car at the top of a hill that is 42 m high.
PE = (1200 kg)(9.8 m/s²)(42 m) = 493,920 J
An apple weighing 1 N falls a distance of 1 m. How much work is done on the apple by the force of gravity?
W = (1 N)(1 m) = 1 J
A crane uses an average force of 5200 N to lift a girder 25 m. How much work does the crane do on the girder?
W = (5200 N)(25 m) = 130,000 J
A science student holds a 0.055 kg egg out a window. Just before the student releases the egg, the egg has 8.0 J of gravitational potential energy with respect to the ground. How high is the student's arm above the ground?
h = 8 J/(9.8 m/s² x 0.055 kg) = 15 m
A 35 kg child has 190 J of kinetic energy after he sleds down a hill. What is the child's speed at the bottom of the hill?
v² = (2 x 190 J)/35 kg = 10.86 v = √10.86 = 3.3 m/s
It takes 1200 J of work to lift a car high enough to change a tire. How much work must be done by the person operating the jack if the jack is 25% efficient?
work input = (1200 J)/(0.25) = 4,800 J
A windmill has an efficiency of 37.5%. If a gust of wind does 125 J of work on the blades of the windmill, how much output work can the windmill do as a result of the gust?
work output = (125 J)(0.375) = 46.9 J
A 65 kg rock climber ascends a cliff. What is the climber's gravitational potential energy at a point 35 m above the base of the cliff?
PE = (65 kg)(9.8 m/s²)(35 m) = 22,295 J
How much potential energy does a 65 kg climber have at the top of Mount Everest (8800 m high)?
PE = (65 kg)(9.8 m/s²)(8800 m) = 5,605,600 J
A mechanic uses a hydraulic lift to raise a 1200 kg car 0.50 m off the ground. How much work does the lift do on the car?
W = (1200 kg)(9.8 m/s²)(0.50 m) = 5880 J
A bicycle's brakes apply 125 N of frictional force to the wheels as the bike moves 14.0 m. How much work do the brakes do?
W = (125 N)(14.0 m) = 1750 J
A bowling ball traveling 2.0 m/s has 16 J of kinetic energy. What is the mass of the bowling ball in kilograms?
m = (2 x 16 J)/(2 m/s)² = 8 kg
A diver has 3400 J of gravitational potential energy after climbing up onto a diving platform that is 6.0 m above the water. What is the diver's mass in kilograms?
m = 3400 J/(9.8 m/s² x 6.0 m) = 58 kg