Unit 3 Lesson 1
Exercises
1. A person pushes a 10.0 kg mass at constant speed across a µ=0.150, 8.50 m
long floor at constant speed. a) how much work does the person do? (125 J)
b) how much work does friction do? (-125J)
2. a) Find the power required for a crane to lift a 400. kg mass (at constant
speed) 100. metres in 30.0 seconds.
(13100 W)
b) if the crane consumes 35 kW of electrical power, find its efficiency (37%)
3. Find the rate at which work is done if in 20.0 seconds a person drags a 30.0
kg block at constant speed across a 10.0m long floor with µ=0.0200 (2.94 W)
4. A 9.00 kg mass is pulled up a 25.0° frictionless incline at a constant speed of
1.50 m/s a) what force is required (37.3 N) b) what power is required (55.9 W)
5. A 1100kg car can accelerate from 0.0 to 60. kph in 6.5 seconds. With constant
engine power, what is the steepest hill the car could climb at 20. kph? (23°)
6. A person pulls on a 20.0 kg lawnmower with a force of 25.0 N and moves the
mower 4.50 metres. The handle angle is 15.0° with the horizontal and µ=0.100.
Find a) work done by person
b) work done by friction c) the time
(109J, -85.3J, 5.89s)
7. a) How much work is done lifting a 50.0kg barbell up one metre? (490.J)
b) if the person actually used 2.40 kJ of food energy, find the efficiency of
their muscles (20.4%)
8. A person pushes with 75.0N on a lawnmower, which has a handle angle of
20.0° and a mass of 25.0 kg. The surface has µ=0.210 and is 30.0 m in length. The
mower starts at rest. Find a) rate at which heat energy is generated (162 J/s)
b) final speed of the lawnmower (5.72 m/s)
9. Consider the task of moving a 250. kg piano from ground level 1.50 metres up
into a moving van. The van has an 8.00 metre long frictionless ramp.
a) find the force required to lift it straight up (constant speed)
(2450 N)
b) find the force required to push it up the ramp at constant speed (459 N)
c) find the mechanical advantage of the ramp
(F ramp /F lift =5.33)
10. On a stairclimber at the gym, a 60. kg person lifts their centre of mass up
20. cm with each step. if they take 300 steps in 6.0 minutes and their muscles
are 20.% efficient then find
a) the rate at which the person does work (98 W)
b) the rate at which the person uses food energy (490W)
11. A person pushes a 10.0 kg mass up a 7.60 m long, 20.0° ramp (µ=0.170) with a
horizontal force of 70.0 N. Find the work done by the person and the heat
energy generated by friction.
(500.J; 150. J)
70.0 N
10.0 kg
20.0°
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Unit 3 Lesson 2
Exercises
1. Find the work done when a k= 10. N/m spring is stretched from 0.0 m to 1.2m
(7.2 J)
2. Find the work done in stretching the spring whose force-distance graph is
shown below
a) 0.0 cm to 4.0 cm
b) 0.0 cm to 10. cm
c) 4.0 cm to 10. cm
d) 2.0 cm to 8.0 cm
(1.8 J; 4.2 J; 2.4 J; 3.3J)
60 N
5 cm
10 cm
3. Find the slope of this work-displacement graph(with units) and interpret it
slope =
2.0 J
5.0 m
what slope tells us:
(0.40 J/m or 0.40 N of force acts on the object)
4. A negative force value indicates a change in force direction. A section of the
graph under the axis corresponds to 'negative work'.
On the graph below, find the work done in moving the object from
a) 0 to 3 m
b) 0 to 6 m
c) 0 m to 10 m d) 6 m to 10 m
100 N
5m
10 m
-100 N
(200 J, 400 J,100 J,-300J)
5. A spring has constant of 15.0 N/m
a) find the work done stretching it from x= 0.0 to 3.0m
c) find the work done stretching it from x=3.00 to x=7.75m
Physics 12 Student Workbook
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(68 J)
(383 J)
158
6. The graph below shows the force applied to a 50 kg object on a flat surface.
What will be the work done in moving it from x=0m to x = 5m? (400J)
100 N
force versus
position
2m
5m
7. A person pushes on a 20.0 kg lawn-mower with 32.5 N and moves it 10.5 m.
The handle of the lawn-mower in inclined at 35.0° above the horizontal and
the rolling friction coefficient is µ=0.100. Find
a) amount of work done by person (280. J)
b) amount of heat energy generated by friction (225 J)
c) rate at which the person does work (31.0 Watt)
d) the final speed of the lawn-mower (2.33 m/s)
8. A 6.50 kg mass is pulled up a 10.0 metre long 8.75° frictionless incline at
constant speed of 1.50 m/s. Find
a) the force required
(8.90 N)
b) the work done
(89.0 J)
c) the power required
(13.3 Watt)
9. What power motor is required to lift 1200 kg steel girders to the top of a 30.
metre high structure in 1.5 minutes? (3900 Watt)
10. A 1200. kg car can move up a 10.00° incline at a max speed of 15.00 m/s. At
this speed, the drag force on the car is 7000. N. Find
a) the force of propulsion from the car's wheels (9042 N)
b) the power of the car's engine (13 560 Watt=181.8 hp)
11. A 1000. kg car has a maximum power output of 100. horse-power (1 hp = 746
Watt). How steep a hill can it climb at constant speed of 60.0 km/hr if frictional
forces add up to 500. N? (23.9°)
12. A person pushes on a wall. The wall bends slightly under this force, and the
person holds the wall in this slightly bent position. Which of the following is
the best answer to the question: "Is any work being done?"
A) No. There is no displacement, and therefore no work
B) Yes. The person's arms get tired so they must be doing work
C) No. Work is done in bending the wall, but not once the wall is held in
the bent position
D) Yes. Although there is no displacement of the wall, the force is large
and so there is still work done
Physics 12 Student Workbook
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Unit 3 Lesson 3
Exercises
1. A person throws a baseball horizontally
a) write a work/energy equation
b) How much work is done throwing a 175g baseball at 30.0 m/s?
c) if you use 350. J of food energy in throwing the ball, what is the
efficiency?
(W=KE; 78.8J; 22.5%)
2. A student goes on a hike and climbs a mountain
a) write a work/energy equation
b) How much work is done if a 50.0 kg student climbs an 800. m high
mountain?
c) if the student's muscles are 15% efficient, how much food energy is
needed?
d) how many 320 kJ chocolate bars would be required to supply this
food energy?
(W=PE; 392 kJ = 3.92 × 105J ; 2.6 × 106 J; 8.2)
3. A 220 kg dolphin jumps through a hula hoop held 4.0 metres above the
water's surface. If we ignore the dolphin's horizontal speed and take its muscle
efficiency to be 35%, then how much food energy does the dolphin use? (25kJ)
4. A 1000. kg car speeds up from rest to 15.0 m/s in 4.00 seconds at constant
acceleration.
a) write a work/energy equation
(W=KE)
b) what is the net work done?
(113 kJ= 1.13 × 105 J)
c) if 80. kJ of heat were lost to the road and 75 kJ each to sound and air
friction, then what is the energy used by the car's engine? (342 kJ)
d) what is the average power of the car's engine?
(85.6 kW)
e) what is the efficiency of the car's engine? (32.8%)
5. A 1000. kg horse speeds up at constant power of 1.0 horsepower (746 Watts)
starting from rest.
a) What speed does the horse reach after 12 seconds?
(4.2m/s)
b) what is the force exerted by the horse at t= 12 seconds
(180 N)
6. How much work is done if a 75.0 kg backpacker walks 10.0 km to reach the
top of a 2.00 km high mountain?
(1.47 MJ = 1.47 × 106 J )
7. In #6, find the power required if the walk takes 3.00 hours.(136 W)
8. How much power is required to lift a 50.0 kg mass at constant speed of 2.50
m/s? (1220 W)
9. A 10.0 kg mass is pulled at constant speed up a frictionless 20.0° incline to a
maximum height of 20.0 metres above the ground.
a) what force is required to pull the mass up?
(33.5N)
b) how long is the ramp?
(58.5m)
c) how much work was done?
(W=Fd)
(1960 J)
d) write a work/energy equation
(W=PE)
e) how much work was done?
(W=∆E)
(1960 J)
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10. A ball is thrown from ground level and when it is 6.00 metres above the
ground, it is moving at 5.00 m/s.
a) write a work/energy equation
b) Find the work done on the ball if it has mass 150. grams.
(W= PE + KE; 10.7 J)
11. An upwards force of 22.0 N acts on an initially stationary 1.20 kg object. As
the object rises vertically 10.0 m, it loses 50.0 J of energy due to air drag.
a) write a work/energy equation
( 0 + Wpush + Wdrag = KE + PE)
b) fidn the final speed of the object
(9.34 m/s)
12. If we have data for PE of an object versus its weight (mg), then what will
the slope of the graph tell us?
13. Which of the following best represents the kinetic energy of a freely
falling object as a function of time?
KE
KE
KE
t
i
KE
t
t
ii
iii
t
iv
Using principles of physics, explain your answer
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14. Find
a) the acceleration of this system
b) the tension in the cord supporting the pulley
(2.15m/s2)
(38.2 N)
cord
the pulley has no mass
2.50 kg
1.60 kg
15. A projectile is launched on level ground at 25.0 m/s and 19.0°. Find
a) the speed at the top
(23.6 m/s)
b) the maximum height
(3.38 m)
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Unit 3 Lesson 4
Exercises
1. Tarzan has mass 85.0 kg and he runs at 6.00 m/s. He grabs onto a vine and
swings up until he stops. a) write a work/energy equation
b) how high can he swing?
( KE=PE; 1.84m)
2. A 22.0 kg child slides down a rough ramp. At the bottom of the 5.00m high
ramp, the child has speed 2.50 m/s. a) write a work.energy equation
b) Find the energy lost due to friction
(PE+W=KE OR PE=KE+heatE;-1010J)
3. A water fountain shoots water straight up 5.20 metres into the air.
a) write a work/energy equation
b) What is the speed of the water when it leaves the fountain?
(KE=PE; 10.1 m/s)
4. A 500. kg roller coaster is moving at 1.20 m/s the top of a 30.0m high hill.
Assuming no friction, what will be the speed of the coaster when it zooms
down the hill and is at height
a) 25.0 m
b) 12.0 m
c) 0.00m
(9.97 m/s;18.8 m/s; 24.3 m/s)
5. A 1200 kg car moving at 10. m/s speeds up to 20. m/s. The car's engine is 18%
efficient.
a) write a work/energy equation
b) how much gasoline chemical energy was used?
(KE + W= KE; 1.0 MJ)
6. A 1000. kg car moving at 108. kph jams on its brakes and comes to a stop.
a) write a work/energy equation b) How much work is done by friction?
(KE+W=0 OR KE = heatE; -450. kJ)
7. An 800. kg bucket is attached to a cable and pulled upwards so that it
accelerates from rest upwards at 1.30 m/s2 for a distance of 30.0 metres
a) write a work/energy equation
(W=PE+KE)
b) find the cable tension
(8880 N)
c) find the speed of the bucket after 30 metres
(8.83 m/s)
d) find the work done by the applied force (Fd)
(266 kJ)
e) find the work done by the applied force (∆E)
(266 kJ)
8. Which of the following graphs relates the amount of kinetic and potential
energy for a freely falling object?
KE
KE
KE
i
PE
KE
PE
ii
PE
iii
PE
iv
Using principles of physics, explain your answer
Physics 12 Student Workbook
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172
9. Some years ago, a 80.0 kg paratrooper fell out of a plane at an altitude of 270.
metres and fell without a parachute to the ground below. When they landed,
they made a 1.10 metre deep crater in the snow, but they survived! Assume that
due to air resistance they were moving at 50.0 m/s when they hit the ground.
vi=0
v=50 m/s
v=0 m/s
a) write a work energy equation describing their fall from the plane to
ground level (take ground level to be h=0; ignore the initial KE)
b) find the work done by air friction during the fall
c) write a work energy equation describing the slowing down in the snow as
they hit the ground (take ground level to be h=0)
d) find the work done by the snow during the impact
e) find the average force from the snow
(PE+ W = KE OR PE= KE + heatE; -112 kJ; KE+W =PE ; -101 kJ; 91.7 kN=9.17×104 N)
10. A toy car of mass 5.0 kg is pushed and given an initial speed of 6.0 m/s
upwards on a 30° ramp. If the friction force opposite to the motion is 4.0 N,
find how far along the ramp the car goes before stopping
a) solve using force and acceleration
(3.2 m)
b) solve using energy
(KE+W=PE; same answer)
11. A mass m is thrown horizontally at 5.00 m/s off of a 20.0 metre high cliff.
Find its speed at impact
a) using projectile analysis
(20.4 m/s)
b) using energy analysis (note m cancels from equations!)
12. An escalator lifts 60 people per minute (avg 60. kg each) to a height of 10.
metres. What power motor is required?
(5900 Watts)
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Unit 3 Lesson 5
Exercises
1. How do seatbelts and air-bags protect car drivers in a collision? (hint: the
egg example is a good analogy)
2. A 1000. kg car moving at 30. m/s hits a tree and stops in 0.25 seconds. Find
a) the change in momentum of the car
(30 000 kgm/s)
b) the force on the car
(120 000 N)
3. A 3.20 kg mass moving at 4.00 m/s East hits a wall. The wall exerts a force of
250. N to the West for 0.0700 seconds. Find the final speed and direction of the
mass.
(1.47 m/s West)
4. A rifle accelerates 10.0 gram bullets from rest to 200. m/s. The rifle barrel is
about 1.20 metres long. Find a) the impulse acting on the bullet (2.00kgm/s)
b) the force on the bullet
(167 N)
5. A 45 gram pinball moving at 0.50 m/s hits a bumper and rebounds at 0.75
m/s. if this takes 1.2 seconds, find the force that acted on the pinball. (0.047 N)
6. A 12 000 kg jet plane is at rest. In one second, it takes in 120 kg of air and
ejects it at a speed of 80. m/s (relative to the ground). Find
a) the force on the air
(9600 N)
b) the final speed of the jet plane.
(0.80m/s)
7. The graph below shows the work done on a 4.00 kg mass. If the mass starts at
rest, find its speed at position 5.00 metres.
80.0 N
force versus
position
3.00 m
5.00 m
(11.8 m/s)
8. 75 marbles per minute roll of a table and fall to the floor as shown below.
When they hit the floor the 35.0 gram marbles are moving downwards at 7.00
m/s. They rebound upwards at 3.00 m/s. Find the force (averaged over a 1.00
second interval) that the floor exerts on the marbles.
3 m/s
7 m/s
(0.866 N ^j)
Physics 12 Student Workbook
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9. A 15 kg mass is attached to an Atwood machine with 5.0 kg on the other side
as shown below. Find the speed of the system just before the 15 kg hits the
ground
a) solve by force and acceleration
(4.9 m/s)
b) solve by energy
15 kg
2.5 m
5.0 kg
10. Find the flight time and range for this projectile (2.1 s; 41m)
22 m/s
28°
11. Find the acceleration of this mass if it is
a) sliding down the ramp
(2.66 m/s2)
b) sliding up the ramp.
(5.00 m/s2)
µ=0.130
5.00 kg
23.0°
12. A baseball is hit by a bat. The following graph shows how the force on the
ball varies as a function of time. Find the area under the graph (with units)
and interpret.
(6750 kgm/s or Ns )
force
(N)
1500.
1000.
500.0
5.00
Physics 12 Student Workbook
©Donald J. Mathewson 2002
time (sec)
180
Unit 3 Lesson 6
Exercises
1. The diagram below shows two pop cans of unequal mass. initially at rest. An
explosive charge is detonated between them and the cans fly apart.
m
2m
m
before = at rest
2m
after =exploding apart
a) What can be said about their velocities after the explosion?
___________________________________________________________________
___________________________________________________________________
b) Using principles of physics, explain your answer
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
2. Find the unknown velocity in each case (the numbers in the circles are kg)
before
4.0
60 m/s
after
v
4.0
1.0
1.0
(ans v=48)
4.0
12 m/s
2.0
4.0
4 m/s
v
2.0
(ans v=16)
4.0
3 m/s
1.0
v
4.0
1.0
(ans v=12)
6.0
10 m/s
2.0
6.0
2m/s
v
2.0
12 m/s
(ans v=12)
Physics 12 Student Workbook
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3. A 5 kg cannon ball experiences a force of 50 000 N and emerges from the
barrel moving at 200 m/s. Find
a) impulse on the ball
b) time the force acts on the ball (1000 Ns; 0.02 sec)
4. A 150. gram ball is thrown at a baseball player at 50.0 m/s. The player hits it
with an impact that lasts 0.0100 seconds and the ball moves in the opposite
direction at 100. m/s. Find the force that acted on the ball.
(2250 N)
5. An arrow moving at 40.0 m/s hits and sticks into a 400. gram apple. After the
collision, apple and arrow are moving together at 10.0 m/s. What is the mass of
the arrow? (133 grams)
6. A nucleus of uranium originally at rest disintegrates into two smaller
nuclei. The larger piece moves at 23 000 m/s. The smaller piece has 1/60. the
mass of the larger. How fast is the smaller piece moving and in what direction?
(1.4 × 106 m/s; opposite to larger)
7. A 1200. kg car moving at 35 kph runs into and sticks to a parked 1000. kg car.
The collision takes 0.15 seconds and after the crash the cars wheels lock and
they skid to a stop on the µ=0.40 road. Find
a) the final speed of both cars
b) the distance travelled before skidding to a stop
c) the impact force on both cars
d) the energy absorbed in the crash
(5.3m/s; 3.6m; 35kN= 35000 N; 26kJ)
8. A 5.00 kg mass is launched upwards at 8.00 m/s. It hits and sticks to a
stationary 4.00 kg block which is held 2.00 m above the ground
a) how fast is the 5 kg mass moving just before the impact (4.97 m/s)
a) how fast are the two masses moving together after the crash? (2.77 m/s)
b) how high does the combined mass go? (0.39 m higher; 2.39m in total)
9. A 10. kg mass is moving right at 4.0 m/s. A 5.0 N braking force acts on the
mass for 3.0 seconds. Find
a) the initial momentum b) the change in momentum / impulse
c) the final momentum
d) the final speed
4 m/s
10 kg
(40. kgm/s;-15 kgm/s ;25kgm/s ;2.5m/s)
10. You may have seen large yellow containers on the highways at exit ramps.
These containers are filled with sand or water. Newer containers have a loose
top half resting on a bottom. These containers are designed to protect cars that
would otherwise hit solid concrete barriers. How do these containers (called
'impact attenuators) work?
11. A 1000 kg car moving at 20 m/s East hits a 2000 kg truck moving at 10 m/s
West. The vehicles stick together. Assume that the system is perfectly closed.
a) find the final velocity of the car and truck
(0m/s)
b) show that the collision changes the energy of the system.
c) why do the collision forces change the energy of the system, but not the
momentum?
Physics 12 Student Workbook
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188
Unit 3 Lesson 7
Exercises
1. When you fire a gun, the rifle recoils and hits your shoulder. Explain why
this happens.
rifle recoils when fired
2. Fill in the chart below
mass
velocity
3.0 kg
→
p (polar)
^
{3.0î + 2.0j
} m/s
3.1 m/s, 40.° E of S
7.5 kg
0.50 kg
→
p (components)
{5.0î + 2.0j} kgm/s
^
(9.0î+6.0j kgm/s; 11 kgm/s at 34°NofE;
^
10î+4.0j m/s; 5.4 kgm/s at 22°NofE)
^
15î-18j kgm/s; 23 kgm/s at 40.°EofS;
3. Find the momentum change and force vectors if
a) A 2.0kg mass initially moving at 2.0 m/s N changes to 3.0 m/s East in 2.0 s.
b) A 5.0 kg mass moving at 5.0 m/s 30.°E of N changes to 2.0 m/s North in 3.0 s
(7.2 kgm/s at 34°SofE; 3.6 N at 34°SofE ; 17 kgm/s at 43°SofW; 5.7 N at 43°SofW)
4. a) write equations for horizontal and vertical momentum
b) Find the unknown speed v and direction
c) find KE loss in collision
v
5.0
5.0
2.0 m/s
2.0
2.0
4.0m/s
4.0 m/s
( 2×4 + 5×0 = 2×0 + 5×v x ; 2×0 + 5×(-2) = 2×(-4) + 5×v y; 1.6 m/s at 14° S of E; 3.2 J)
5. A 2000. kg car moving east at 14.0 m/s collides with a 4400. kg truck moving
south at 10.0 m/s. The vehicles stick together. In what direction do they head
after the crash? Solve by graphical addition of vectors
( 57.5° S of E)
6. A steel ball of mass 10.0 kg is moving East at 5.00 m/s. It hits a rubber ball of
mass 5.00 kg moving at 10.0 m/s due North. After the crash, the steel ball is
moving at 4.00 m/s, 60.0° E of N and the rubber ball moves at an unknown
velocity.
a) write a horizontal momentum equation
(10×5 + 5×0 = 10×3.46 + 5 vx )
b) write a vertical momentum equation
(10×0 + 5×10 = 10×2 + 5 vy)
c) Find the velocity (and dir'n) of the rubber ball. (6.74 m/s 27.1°E of N)
Physics 12 Student Workbook
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7. Write momentum equations in terms of given variables.
v
m
m
vi
θ
M
M
at rest
φ
u
( mvi=mvcos(θ) + Mucos(φ)
mvsin(θ)=Musin(φ) )
8. Two people are in a 160 kg life raft, floating motionless on the sea. If one
person (55 kg) dives off the raft heading to the East at 4.4 m/s, and the other
person (72 kg) dives off the raft heading North at 4.2 m/s.
a) write a horizontal momentum equation
b) write a vertical momentum equation
c) What will be the speed and direction of the 160 kg raft?
( 0= 55×4.4 + 72×0 + 160vx ; 0= 55×0 + 72×4.2 + 160vy; 2.4 m/s at 51°S of W )
9. Solve #8 using a vector diagram. Note that since the total initial momentum
was zero, the total final momentum must also add to zero.
10. A 2.00 kg mass moving East at 4.00 m/s hits a stationary 3.00 kg mass. After
the collision, the 2.00 kg mass is moving at 3.70 m/s at a heading of 15.0° N of E.
If the crash took 0.0200 seconds, find the collision force (&dir'n).
(105 N at 66.0° N of W)
11. In the collision pictured below, the 1.0 kg mass is initially at rest. Find
a) the components of the unknown velocity v
(2.9 î + 1.7 j)
b) the magnitude and direction of v
(3.3 m/s 30.° N of E)
c) the KE loss in the collision
(6.7 J)
v=0
1
v
4m/s
5
30°
5
1
12. Solve #11 using a vector drawing. Note that in this case, there are no
vectors to add!
13. A 50.0 kg object has a speed of 30.0 m/s North. A force acts on it and the
momentum change (impulse) is 1000. kgm/s at 30.0° N of E. Find the final
velocity of the object.
(17.3i + 40 j = 43.6 m/s at 66.6° N of E)
Physics 12 Student Workbook
©Donald J. Mathewson 2002
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Unit 3 Lesson 8
Exercises and Review
1. A 1.0 kg mass moving at 10. m/s hits and sticks to a 5.0 kg mass.
a) how fast are the masses moving after the crash? (1.7 m/s)
b) how much work was done during the collision? (-42J)
10 m/s
1 kg
5 kg
1 kg
5 kg
2. A 30.0 gram bullet moving at speed 330. m/s hits a 3.00 kg ballistic pendulum.
The bullet passes through the ballast and exits at 90.0 m/s. To what height does
the pendulum swing?
(0.294 m)
3. A tennis ball machine launches 3 balls each second at a wall. The 70. gram
balls hit the wall moving horizontally at 20. m/s, and rebound at 15 m/s. Find
a) the average force on the wall.
(7.35 N)
b) the energy absorbed by the wall
(6.12 J)
4. The 2.0 kg mass below starts at rest and slides down the frictionless ramp. It
then hits and sticks to a stationary 5.0 kg mass and together they fly off the
table. Find the horizontal distance travelled before hitting the ground.(3.6 m)
2 kg
20. m
5 kg
2.0 metres
R=?
5. Air bags inflate very quickly when a car collision occurs. Once inflated,
they deflate just as quickly. Why is this important ?
6. A 2.00 kg mass initially at rest slides down a frictionless 5.00 m high ramp. At
the bottom of the ramp it hits and sticks to a stationary 3.00 kg mass. Find the
final speed of both masses.
(3.96 m/s)
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7. A 2.20 metre long pendulum is tied to the ceiling in a 3.0 metre high room. A
5.00 kg mass tied to the end is released from a 20.0° angle. At the bottom of its
swing the mass is moving at 1.42 m/s. Find the energy loss due to friction and
the efficiency of the process.
(1.46J; 77.5%)
2.2 m
20°
2.2m
v=0
room
8. A 60.0 kg box starts at rest and is pulled with a constant 100. N force across a
10.0 m frictionless floor and then across a 10.0 m long mu=0.200 floor. Find the
final speed of the box.
(5.24 m/s)
9. Why do we follow through when we make a stroke in golf, tennis, baseball?
10. A 5.00 kg mass is launched at an angle of 45.0° at a speed of 10.0m/s. At the
top of its path, the 5.00kg mass explodes into two pieces: a 1.00 kg bit and a 4.00
kg bit. The 1kg bit is momentarily at rest after the explosion. Find where the
4kg and 1 kg bits land relative to the original launch point.
(1kg: 5.10 m from launch point; 4 kg: 11.5 m from launch point)
11. An air puck of mass 2.00 kg moving at 1.60 m/s and 80.0° N of E collides with
a 1.00 kg air puck of unknown velocity. After the crash, the 2.00 kg is moving
at 1.64 m/s 3.30° W of N and the 1.00 kg is moving at 0.596m/s 62.0° NofE. Find
the initial speed of the 1.00 kg.
(0.788 m/s at 55.5°NofW)
12. Is it easier to hit a home-run off of a fast pitch or off of a slow pitch?
slow pitch
fast pitch
baseball bat
a) fast pitch
b) slow pitch
c) both the same
Using principles of physics, explain your answer
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Lesson 9: Practice Exam
Section I. Multiple Choice. (30 marks)
1. A 2.0 kg mass with velocity of 3.0 m/s collides with a stationary 5.0 kg mass
and rebounds in the opposite direction at 1.0 m/s. What is the final speed of the
5.0 kg mass?
a) 8.0 m/s b) 1.6 m/s c) 0.80 m/s d) 40. m/s e) 4.0 m/s
2. A 500 kg cannon fires a 10 kg ball at 20 m/s. What is the change in
momentum of the cannon?
a) 0.4 m/s
b) 200 kgm/s
c) 50 Ns
d) 10 000 kgm/s
e) 2 kgm/s
3. A 5.0 kg mass moving North at 3.0 m/s experiences a completely inelastic
collision with a 2.5 kg mass. How much kinetic energy is lost in the collision?
a) 15 J
b) 1.0 J
c) 7.5 J
d) 2.0 J
e) 23 J
4. A 2.0 kg mass moving East at 3.0 m/s collides with a 3.0 kg mass moving
North at 2.0 m/s. The collision is completely inelastic(the masses stick
together). Find final speed of both masses.
a) 1.0 m/s b) 6.0 m/s c) 2.4 m/s d) 1.7 m/s e) 1.2 m/s
5. A 2.0 kg mass moving at 4.0 m/s East experiences a force of 3.0 N North for
2.0 s. What is its final speed?
a) 5.0 m/s
b) 7.0 m/s
c) 10. m/s
d) 1.0 m/s
e) 3.0 m/s
6. Why is momentum conserved in (closed system) collisions?
a) the system is closed
b) the system is conservative
c) gravity does no work
d) momentum is transferred to the surroundings
e) equal and opposite forces
7. What is an elastic collision?
a) one where no momentum is lost
b) one where no kinetic energy is lost
c) an imaginary collision
d) a collision where objects stick together
e) a collision where the objects deform and absorb elastic energy
8. In a crash between a car and truck, what is the main reason the truck driver
is better off than the car driver?
a) the car has more speed
b) the truck has more momentum
c) the truck has more mass
d) the truck is larger
e) the truck is more strongly built
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9. A mass is moving east. A force is briefly applied to the mass in a northerly
direction. After the force has been applied, in what direction does the mass
move?
during
v
before
after
v
F
a) north of east
b) east
c) north
d) north of west
************10, 11 and 12 relate to this picture************
2.8 m/s
3.0 m/s
4.0 kg
4 10.°
5.0 kg
5
v
10. What is the final vertical speed of the 5 kg?
a) 0.48 m/s
b) 0.60 m/s c) 2.8 m/s
d) 2.2 m/s
e) 0.39 m/s
11. What is the final horizontal speed of the 5 kg?
a) 0.19 m/s
b) 3.0 m/s
c) 2.76 m/s
d) 0.24 m/s
e) 0.97 m/s
12. What is the change in momentum (magnitude) of the 4 kg mass?
a) 2.2 kgm/s
b) 1.9 kgm/s
c) 0.97 kgm/s
d) 0.80 kgm/s
e) 0.20 kgm/s
13. Which of the following is false ?
a) work is force times displacement
b) work produces an energy change
c) work is power over time
d) work is average force times displacement
e) work is positive and negative
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14. A 6.0 kg mass is on top of an 80. m high office building. What is the
potential energy of the ball relative to a construction platform which is 20.m
off the ground?
a) 3.5 × 102 J b) 4.7 × 102 J c) 1.1 × 103 J d) 3.5 × 103 J e) 4.7 × 103 J
6 kg
80 m
20 m
15. A 2.0 kg ball is 5.0 m above the ground and is moving at 5.0 m/s. What is its
total energy?
a) 50 J
b) 25 J
c) 75 J
d) 120 J
e) 100 J
16. Using the following graph of Force vs position, find the work done in
moving an object from 0.00 to 5.00 m.
F
o
r
c
e
(N)
200.
100.
position(m)
5.00
a) 1.00×103 J
b) 700. J c) 300. J d) 400. J e) 500. J
17. If the graph in question #16 represents the work done on a 4.00 kg mass,
find the speed of the mass when it reaches x= 5.00 m. The mass is initially at
rest.
a) 18.7 m/s b) 15.8 m/s
c) 22.4 m/s d) 14.1 m/s e) 12.2 m/s
18. A girl exerts a 200. N force to lift a barbell to a vertical height of 2.0 m in
5.0 s. If she had done this in 10.0 s, the work done would have been
a) 4 times as great b) twice as great c) the same d) half as great e) one
quarter as great
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19. A 30.0 kg lawnmower is pulled with a force of 200. N along its 30.0° handle.
If there is 20.0 N of friction on the mower, find the work done (by the person
only, not including friction) in moving it 5.00 m.
200 N
30°
20 N
a) 1.00×103 J b) 900. J c) 500. J d) 766 J e) 866 J
20. A mass slides across a frictionless surface. Which of the following best
explains why no work is done?
a) motion is horizontal, forces are perpendicular to the motion
b) work is done, but the total work is zero
c) because there is no friction
d) because gravity never does work
e) because the normal force affects the direction of motion and not the energy
21. The escalator shown below is used to move 20 passengers a minute to the
second floor, which is 5 m above the first. Assume the average passenger mass
is 60 kg
10 m
5m
What approximate power must the escalator motor be able to provide?
a) 100 W b) 200 W c) 1000 W d) 2000 W e) 60 000 W
22. What force and power are required to move a 10. kg mass up a 10.° incline
at a constant speed of 2.0 m/s?
force
power
2 m/s
10
a)
98 N
49 W
b)
49 N
190 W
c)
17 N
9.0 W
d)
97 N
190 W
e)
17 N
34 W
10°
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23. How much work is required to stop a 1200 kg car moving at 10. kph?
a) 60. kJ= 60000 J
b) 4600 J
c) 12 kJ
d) 9200 J
e) 30. kJ
**24 and 25************************
Tarzan (75 kg) swings from his vine from a height of 2.5 m. At the end of his
swing, he is only 2.4m above the ground.
2.4 m
2.5 m
v=?
24. How much work has been done by friction?
a) 74 J b) 176 J c) 81 J d) 21 J e) 18 J
25. If there were no friction, what would be Tarzan's velocity v at the bottom of
the swing?
a) 21 m/s b) 22 m/s c) 11 m/s d) 7.0 m/s e) 6.9 m/s
26. A roller coaster car of mass 1000. kg starts from rest 18 m above ground. It
drops to the ground and then climbs a 10.m high hill. How fast is it going at the
top of the hill?
v=?
18 m
10 m
a) 12 m/s b) 4.2 m/s c) 8.9 m/s d) 19 m/s e) 14 m/s
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27. How much work did gravity do in #26?
a) 0.0 J since gravity conserves energy
b) 0.0 J since gravity force is perpendicular to motion
c) 98 000 J
d) 180 000 J
e) 78 000 J
****** 28 to 30 *************
A 3.0 kg mass is released from rest. It slides down a frictionless ramp and hits a
stationary 4.0 kg mass. The collision is inelastic.
3.0 kg
2.5 m
3.0 kg
4.0 kg
v
28. Which quantities are conserved as the 3.0 kg mass moves down the ramp?
a) kinetic energy
b) momentum
c) kinetic energy and momentum
d) system energy
e) system energy and momentum
29. Which quantities are conserved in the collision between the two masses?
a) kinetic energy
b) momentum
c) kinetic energy and momentum
d) system energy
e) system energy and momentum
30. In #28, if the 3.0 kg mass is at rest after the collision, what is the final
speed and energy of the 4.0 kg mass?
speed(m/s)
energy(J)
a)
6.0
74
b)
7.0
74
c)
5.2
74
d)
5.2
55
e)
5.2
18
1
b
2
b
3
c
4
d
5
a
6
e
7
b
8
c
9
a
10
e
11
a
12
a
13
c
14
d
15
d
16
b
17
a
18
c
19
e
20
a
21
c
22
e
23
b
24
a
25
d
26
a
27
e
28
d
29
b
30
d
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Section II: Written Problems (20 marks total)
1. (5 marks) A 10.0 g bullet moving at 300. m/s hits and passes through a 2.20
kg pendulum target. After the impact, the 1.20 m long pendulum rises up to an
angle of 15.0°. Find the final speed vf of the bullet.
(103 m/s)
15°
1.2 m
vf = ?
300 m/s
2. (5 marks) Tarzan (75 kg) and Jane (50 kg) are going for a swim. They swing
down on vines and fall into the water, Jane lets go at the bottom of the swing.
Tarzan holds on for a little longer and then falls into the water. If we ignore
air resistance, then what can we say about their speeds when they hit the
water? Assume their vines have equal length
a) Jane is moving faster when she hits the water
b) Tarzan is moving faster when he hits the water
c) they are both moving at the same speed when they hit the water.
tree branch
vine
Tarzan
Jane
Tarzan holds on
for a little longer
Jane lets go at
bottom
water
Using principles of physics, explain your answer
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
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3. (5 marks)A 2.00 kg mass moving at 4.00 m/s North hits a stationary 6.00 kg
mass. The collision takes 0.0250 seconds. After the collision, the 2.00 kg mass is
moving at 3.80 m/s and 10.0° W of N.
a) find the final speed and direction of the 6 kg mass
b) draw a vector diagram showing initial and final momenta
c) find the force on the 2.00 kg mass during the collision
6v
(0.236 m/s at 21.3° N of E;
56.7 N at 21.3° S of W)
8 kgm/s
7.6 kgm/s
10°
4. (5 marks) A 10.0 kg mass is pulled from rest up a 15.0° inclined plane. The
plane has friction coefficient µ=0.260. The mass starts at the bottom of the ramp
and is pulled 20.0 metres along the ramp by a rope which is at 22.0° angle.
There is 65.0 N of tension in the rope. Find
a) the force of friction
b) the work done by the pulling force
c) the work done by friction
d) the speed of the mass at the top of the ramp
65.0 N
22.0°
10.0 kg
mass moves 20.0 m up ramp
15.0°
(18.3N; 1.20×103 J; -366 J; 8.15 m/s)
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Additional (hard) written problems
1. A skier of mass 50.0 kg is on a T-bar, being pulled up the hill at a constant
2.25 m/s. The hill is a 70.0 metre long µ=0.150, 30.0° inclined plane . The T-bar
is at a 40.0° angle
a) what motor power is required?
(617 Watt)
b) how much work is done by the T-bar?
(19.2 kJ)
c) how much work is done by gravity?
(-17.2 kJ)
d) how much work is done by friction?
(-2.0 kJ)
T-bar cable
40°
30°
2. Although we often treat cars as accelerating at constant force, it is actually a
better approximation to say they accelerate at constant power (since the car
engine uses a constant Joules per second of gasoline chemical energy).
If a car of mass m starts at rest and accelerates at constant power P, then
a) find an expression for its speed at time t.
b) sketch a graph of velocity versus time
3. If the following force acts on a 250. kg motorcycle moving up a 100. m long
10.0° incline, find its final speed at the top assuming the motorbike starts at
rest and that no energy is lost to friction
(5.06 m/s)
force
460. N
435 N
distance
along ramp
20.0 m
100.m
4. On a flat frictionless skating rink, a 60.0 kg skater at rest holds a 10.0 kg
medicine ball. He throws it to a stationary 50.0 kg skater, who catches the ball
and then throws it back. In both cases, the ball moves at 1.20 m/s relative to
the ground. After the 60.0 kg skater catches the ball thrown back to him, how
fast are the skaters moving apart? (0.823m/s)
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