Download Questions - CC Physics Don Mitchell

Net Force
Eg1)
Two people are pulling a canoe using separate ropes. Person A pulls at an angle of 30.0º
from the bow with a force of 50.0 N while person B pulls at an angle of 45.0º with a
force of 70.0 N. The force of friction is 15.0 N. Determine the ne t force on the canoe.
Eg2)
A 25-kg store sign is suspended as shown below. Calculate the tensions in the ropes at
the point at which the sign is suspended.
55.0º
Second Law of Motion
Eg1)
Two people are paddling a canoe. Person A has a mass of 70 kg while B has a mass of
75 kg. The canoe has a mass of 20 kg. Person A exerts a force of 400 N [forwards] and B
exerts a force of 420 N [forwards] using the paddles. The magnitude of the water
resistance on the canoe is 380 N. Calculate the acceleration of the canoe.
Eg2)
A person and an elevator have a combined mass of 6.00 x 10 2 kg. The elevator cable has
a tension of 6.50 x 10 3 N [up]. Find the acceleration of the person.
Eg3)
Two masses are connected by a light rope over a frictionless pulley as shown. Determine
the acceleration of the 35 kg mass once the objects are released.
25 kg
35 kg
Eg4)
A 20-kg mass is lying on a horizontal, frictionless surface. The tire is attached to two
light ropes that pass over frictionless pulleys to two hangings masses. Calculate the
acceleration of the 6.0 kg mass.
20 kg
8.0 kg
6.0 kg
WORKSHEET
1)
A 1.0 kg box on a horizontal frictionless surface is accelerated by attaching a 1.5 kg
mass as shown in the diagram. Calculate the acceleration of the 1.0 kg box.
[5.9 m/s 2 right]
1.0 kg
1.5 kg
2)
Two masses of 1.5 kg and 2.0 kg are hung on a frictionless pulley as shown in the
diagram. What is the acceleration of the 2.0 kg mass?
[1.4 m/s 2 downwards]
2.0 kg
1.5 kg
Friction
Eg1)
The magnitude of the applied force on a desk is 165 N angled at 30.0° as shown below.
If the desk remains stationary, calculate the force of static friction acting on the desk.
30.0°
Eg2)
A loonie with a mass of 7.0 g is at rest on an incline of 25.0°. Calculate the force of
static friction acting on the loonie.
Eg3)
A 3.5 kg block is sliding down an incline of 15.0°. The surface of the incline exerts a
force of kinetic friction of magnitude 3.9 N on the block. Calculate the acceleration of
the block.
WORKSHEET
1)
A person tries to push a 50.0 kg crate on a level surface using a force of 100 N
[east]. The crate remains motionless. Determine the force of static friction.
[100 N west]
2)
A 30.0 kg crate is at rest on a 25.0° incline. Determine the force of static friction.
[124 N up the incline]
3)
A 50.0 kg crate is accelerating down a 35.0° incline at 1.25 m/s 2 . Determine the
force of kinetic friction.
[219 N up the incline]
4)
A 70.0 kg crate is being pulled up a 30.0° incline by a rope (acting parallel with the
incline surface) with a tension of 500 N. If the force of kinetic friction is 40.0 N
then what is its acceleration?
[1.67 m/s 2 up the incline]
5)
A 55.0 kg crate is being pulled down a 20.0° incline by a rope (acting parallel with the
incline surface). If it is accelerating downwards at 1.50 m/s 2 and the force of kinetic
friction is 152 N then what is the tension in the rope?
[50 N down the incline]
Static and Kinetic Friction
Eg1)
A sled with waxed hickory runners rests on a horizontal snowy surface. If the coefficient
of static friction between waxed hickory and snow is 0.0060, calculate the mass of the
sled if an applied force of 46 N [forwards] causes the sled to start moving.
Eg2)
A 50-kg sled is on a snowy hill. If the hill forms an angle of at least 20.0° with the
horizontal, the sled just begins to slide downhill. Calculate the coefficient of static
friction for the sled on the snow.
Eg3)
A 1640-kg truck with rubber tires is skidding on wet concrete with all four wheels
locked. If the coefficient of kinetic friction of rubber on wet concrete is 0.50, calculate
the acceleration of the truck.
Eg4)
A person wants to drag a 40-kg sled with a snowmobile up a snowy hill that forms an
angle of 25.0°. The coefficient of kinetic friction for the sled on the snow is 0.040.
Calculate the force the snowmobile must exert to accelerate the sled at 2.5 m/s 2 [uphill].
Newton’s Law of Universal Gravitation
Eg1)
Mount Logan in the Yukon is 5959 m above sea level and is the highest peak in Canada.
What would be the difference in magnitude of the weight of a 55.0 kg person at the top
of the mountain as compared to its base?
Eg2)
Object A exerts a gravitational force of magnitude of 1.3 x 10 -10 N on object B.
Determine the magnitude of the gravitational force if the separation distance is doubled,
the mass of A is increased 6 times, and the mass of B is halved.
Eg3)
During a lunar eclipse, Earth, the Moon, and the Sun are aligned on the same plane as
shown below. If the Moon has a mass of 7.35 x 10 22 kg and the Sun has a mass of
1.99 x 10 30 kg, determine the net gravitational force exerted by both the Moon and the
Sun on Earth.
Moon
Earth
3.84 x 10 8 m
Sun
1.50 x 10 11 m
Gravitational Field Strength
Eg1)
Calculate the magnitude of the gravitational acceleration of a 500 kg object that is 3.00 x
10 4 m above the surface of the Moon? The mass of the moon is 7.35 x 10 22 kg and its
radius is 1.74 x 10 6 m.
Eg2)
a) What is the mass of a 60.0 kg person on Mars and on Earth? The mass of Mars is
6.42 x 10 23 kg and its radius is 3.40 x 10 6 m. The mass of Earth is 5.97 x 10 24 kg and its
radius is 6.38 x 10 6 m.
b) Compared to Earth, how would the person’s weight change on Mars?
Eg3)
A 100 kg astronaut is standing on a scale in a rocket. The acceleration of the rocket is
19.6 m/s 2 [up]. Calculate her true weight and apparent weight during liftoff on Earth.
WORKSHEET
1)
Two students are sitting 1.50 m apart. One student has a mass of 70.0 kg and the other
has a mass of 52.0 kg. What is the gravitational force between them?
[1.08 x 10 -7 N
2)
What gravitational force does the moon produce on the earth if the centres of the earth
and the moon are 3.88 x 10 8 m apart and the moon has a mass of 7.34 x 10 22 kg?
[1.94 x 10 20 N]
3)
If the gravitational force between two objects of equal mass is 2.30 x 10 -8 N when the
objects are 10.0 m apart, what is the mass of each object?
[1.86 x 10 2 kg]
4)
Calculate the gravitational force on a 6.50 x 10 2 kg spacecraft that is 4.15 x 10 6 m above
the surface of the Earth.
[2.34 x 10 3 N]
5)
The gravitational force between two objects that are 2.1 x 10 -1 m apart is 3.2 x 10 -6 N. If
the mass of one object is 5.5 x 10 1 kg then what is the mass of the other object?
[3.8 x 10 1 kg]
6)
If two objects, each with a mass of 2.0 x 10 2 kg, produce a gravitational force between
them of 3.7 x 10 -6 N, what is the distance between them?
[8.5 x 10 -1 m]
7)
What is the gravitational force on a 70.0 kg object standing on the Earth’s surface?
[6.88 x 10 2 N]
8)
Three objects A, B, and C (in that order) are placed 5.00 x 10 -1 m apart along a straight
line. If A and B have equal masses of 10.0 kg and C has a mass of 15.0 kg then what is
the net gravitational force on B due to A and C?
[1.33 x 10 -8 N right]
9)
The gravitational force between two small masses A and B when placed a short distance
apart is 3.24 x 10 -7 N. What is the gravitational force between these objects if the masses
of both A and B are doubled and the distance between them is tripled?
[1.44 x 10 -7 N]
10)
The mass of the Titanic was 4.6 x 10 7 kg. Suppose the gravitational force exerted by the
Titanic on the fatal iceberg was 61 N when the separation distance was 100 m. What was
the mass of the iceberg?
[2.0 x 10 8 kg]
11
Object A exerts a gravitational force of magnitude 5.9 x 10 -11 N on object B. For each
situation, determine the magnitude of the gravitational force:
a) The separation distance increases by a factor of four-thirds, the mass of A increases
by a factor of 1.5, and mass of B is halved.
[2.5 x 10 -11 N]
b) The separation distance decreases by a factor of one-sixth, the mass of A is halved,
and the mass of B increases by a factor of five-fourths.
[1.3 x 10 -9 N]
12)
During the third quarter phase of the Moon, the earth, moon, and sun are positioned as
shown below. Calculate the net gravitational force exerted by both the moon and the sun
on earth.
[ 3.53 x 10 22 N (0.323°) ]
Moon (m = 7.35 x 10 22 kg)
3.84 x 10 8 m
Earth
Sun (m = 1.99 x 10 30 kg)
1.50 x 10 11 m
WORKSHEET
1)
Calculate the gravitational field strength experienced by a 4 30 kg object on the surface of
Mars. Mars has a radius of 3.43 x 10 6 m and a mass of 6.37 x 10 23 kg.
[3.61 N/kg]
2)
At what distance from Earth’s surface is the gravitational acceleration 7.33 m/s 2 ?
[1.01 x 10 6 m]
3)
On the surface of Planet X an object has a weight of 63.5 N and a mass of 22.5 kg.
What is the gravitational field strength on the surface of Planet X?
[2.82 N/kg]
4)
On the surface of Planet Y, which has a mass of 4.83 x 10 24 kg, an object has a weight of
50.0 N and a mass of 30.0 kg. What is the radius of this planet?
[1.39 x 10 7 m]
5)
What is the gravitational field strength 1.27 x 10 7 m above the Earth’s surface?
[1.09 N/kg]
6)
Planet B has a mass of 4.00 x 10 22 kg and a radius of 6.0 x 10 5 m. What is the
gravitational acceleration on the surface of Planet B?
[7.4 m/s 2 ]
7)
What is the weight of a 20.0 kg object on the surface of the moon? The mass of the
moon is 7.34 x 10 22 kg and the radius of the moon is 1.74 x 10 6 m.
[32.3 N (down)]
8)
A 75.0 kg person is on an elevator that is accelerating upward at a rate of 1.00 m/s 2 .
What is his apparent weight?
[811 N (down)]
9)
A person whose true weight is 725 N is in an elevator where he has an apparent weight
of 775 N. Find the acceleration of the elevator.
[0.677 m/s 2 (up)]
10)
If you were on Jupiter, your skeleton would be unable to support your weight. If
Jupiter’s mass is 1.90 x 10 27 kg and has a radius of 7.15 x 10 7 m, then compared to Earth
how many times stronger would your bones need to be? (Find how many times strong er
the acceleration due to gravity is on Jupiter compared to Earth.)
[2.52 times]
11)
Planet Deimos has a mass of 8.68 x 10 25 kg and a radius of 2.56 x 10 7 m. Compared to
Earth, how would a person’s weight change on this planet?
[0.899 times]
12)
A 100 kg astronaut is standing on a scale in a rocket. If it has an acceleration of
19.6 m/s 2 [down] while it is near Earth’s surface then what will be the astronaut’s
apparent weight? What will be the true weight?
[9.79 x 10 2 N (down); 9.81 x 10 2 N (down)]
12)
An 80.0 kg astronaut is leaving the surface of the moon. The acceleration of the rocket is
12.8 m/s 2 [up]. On the moon, the gravitational acceleration is 1.62 m/s 2 [down].
Calculate the magnitude of the true weight and apparent weight of the astronaut.
[True weight is 130 N, apparent weight is 1.15 x 10 3 N]
13)
An astronaut in a rocket has an apparent weight of 1.35 x 10 3 N [down]. If the
acceleration of the rocket is 14.7 m/s 2 [up] near Earth’s surface, what is the astronaut’s
true weight?
[540 N (down)]
14)
How much does an apple with a mass of 100 g weigh if it is 4.00 x 10 6 m above the
surface of the Earth?
[0.371 N]
DYNAMICS REVIEW
1) Forces of 2.0 N [38° N of W] and 3.0 N [61° S of W] act on an object. What is the net
force on the object?
[3.3 N (65° W of S) or (25° S of W)]
2) An object that has a mass of 45.0 kg is pulled along a horizontal surface by a rope that
makes an angle of 32.0° with the horizontal. If the force of friction is 50.0 N and the
tension in the rope is 95.0 N, what is the acceleration of the object?
[0.679 m/s 2 forwards]
3) What is the tension in the cable of a 1.20 x 10 3 kg elevator that is:
a) accelerating downwards at a rate of 1.05 m/s 2
b) accelerating upwards at a rate of 1.05 m/s 2
c) moving downwards at a constant velocity of 1.10 m/s
[1.05 x 10 4 N up]
[1.31 x 10 4 N up]
[1.18 x 10 4 N up]
4) Two people, A and B, are dragging a sled on a horizontal, icy surface with two light
ropes. Person A applies a force of 65 N [30°] on one rope, and person B applies a force
of 70 N [300°] on the other rope. Calculate the net force on the sled.
[96 N (343°)]
5) Two people are pulling a canoe using separate ropes. Person A pulls at an angle of 30.0º
from the bow with a force of 50.0 N while person B pulls at an angle of 45.0º with a
force of 70.0 N. The force of friction is 15.0 N. Determine the net force on the canoe.
[81.6 N (17.4° S of E)]
6) A 25-kg store sign is suspended as shown below. Calculate the tensions in the ropes at
the point at which the sign is suspended.
[1.7 x 10 2 N east and 3.0 x 10 2 N [125°]
55.0º
7) Two people are paddling a canoe. Person A has a mass of 70 kg while B has a mass of 75
kg. The canoe has a mass of 20 kg. Person A exerts a force of 400 N [forwards] and B
exerts a force of 420 N [forwards] using the paddles. The magnitude of the water
resistance on the canoe is 380 N. Calculate the acceleration of the canoe.
[2.7 m/s 2 forwards]
8) Two masses are connected by a light rope over a frictionless pulley as shown. De termine
the acceleration of the 35 kg mass once the objects are released.
[1.6 m/s 2 down]
25 kg
35 kg
9) A 20-kg mass is lying on a horizontal, frictionless surface. The tire is attached to two
light ropes that pass over frictionless pulleys to two hangings masses. Calculate the
acceleration of the 6.0 kg mass.
[0.58 m/s 2 up]
20 kg
8.0 kg
6.0 kg
10) A 1.0 kg box on a horizontal frictionless surface is accelerated by attaching a 1.5 kg m ass
as shown in the diagram. Calculate the acceleration of the 1.0 kg box.
[5.9 m/s 2 right]
1.0 kg
1.5 kg
11) A 70.0 kg crate is being pulled up a 30.0° incline by a rope (acting parallel with the
incline surface) with a tension of 500 N. If the force of kinetic friction is 40.0 N then
what is its acceleration?
[1.67 m/s 2 up the incline]
12) A 55.0 kg crate is being pulled down a 20.0° incline by a rope (acting parallel with the
incline surface). If it is accelerating downwards at 1.50 m/s 2 and the force of kinetic
friction is 152 N then what is the tension in the rope?
[50 N down the incline]
13) A button with a mass of 0.0070 kg is at rest on an incline of 25.0°. Calculate the force of
static friction acting on the button.
[2.9 x 10 -2 N up the incline]
14) A 3.5 kg block is sliding down an incline of 15.0°. The surface of the incline exerts a
force of kinetic friction of magnitude 3.9 N on the block. Calculate the acceleration of
the block.
[1.4 m/s 2 downhill]
15) A sled with waxed hickory runners rests on a horizontal snowy surface. If the coefficient
of static friction between waxed hickory and snow is 0.0060, calculate the mass of the
sled if an applied force of 46 N [forwards] causes the sled to start moving.
[7.8 x 10 2 kg]
16) A 50-kg sled is on a snowy hill. If the hill forms an angle of at least 20.0° with the
horizontal, the sled just begins to slide downhill. Calculate the coefficient of static
friction for the sled on the snow.
[0.36]
17) A 1640-kg truck with rubber tires is skidding on wet concrete with all four wheels
locked. If the coefficient of kinetic friction of rubber on wet concrete is 0.50, calculate
the acceleration of the truck.
[-4.9 m/s 2 forwards]
18) A person wants to drag a 40-kg sled with a snowmobile up a snowy hill that forms an
angle of 25.0°. The coefficient of kinetic friction for the sled on the snow is 0.040.
Calculate the force the snowmobile must exert to accelerate the sled at 2.5 m/s 2 [uphill].
[2.8 x 10 2 N uphill]
19) An eraser of mass 0.0070 kg is placed on the surface of a Physics textbook. A force of
static friction of magnitude 4.40 x 10 -2 N acts on the eraser. Calculate the maximum
angle at which the textbook can be inclined before the eraser begins to slide.
[40.0°]
20) A person pulls a 30 kg sled up a hill shown below. If the coefficient of kinetic friction
for the sled on the hill is 0.50, what force would the person have to deliver in order to
accelerate the sled at 2.0 m/s 2 up the hill?
[3.2 x 10 2 N uphill]
10 m
20 m
21) A 50.0 kg crate lies motionless on a 25.0° incline. Calculate the coefficient of static
friction between the crate and the incline.
[0.466]
22) A 60.0 kg skier accelerates down a 38.0° slope. If the coefficient of kinetic friction
between the skis and the snow is 0.150, then determine the magnitude of the skier’s
acceleration.
[4.88 m/s 2 downhill]
23) A driver of a 1500 kg truck travelling at 30.0 m/s slams on the brakes. If the coefficient
of friction between the tires and the road is 0.600 then determine how long it will take
for the truck to come to a stop.
[5.10 s]
24) A person needs to pull a 40.0 kg crate up a 30.0° incline. If the coefficient of kinetic
friction between the sled and the snow is 0.200 then determ ine the force he needs to
apply to accelerate the sled at 2.00 m/s 2 up the hill.
[344 N uphill]
25) A 100 kg astronaut is standing on a scale in a rocket. The acceleration of the rocket is
19.6 m/s 2 [up]. Calculate her true weight and apparent weight during liftoff on Earth.
[True weight is 981 N, apparent weight is 2.94 x 10 3 N]
26) Calculate the weight of a 6.50 x 10 2 kg spacecraft that is 4.15 x 10 6 m above the surface
of the Earth.
[2.34 x 10 3 N]
27) The gravitational force between two objects that are 2.1 x 10 -1 m apart is 3.2 x 10 -6 N. If
the mass of one object is 5.5 x 10 1 kg then what is the mass of the other object?
[3.8 x 10 1 kg]
28) Object A exerts a gravitational force of magnitude 5.9 x 10 -11 N on object B. Determine
the gravitation force if the mass of object A is quadrupled, the mass of object B is
tripled, and the distance between them is reduced by a factor of two -fifths.
[4.4 x 10 -9 N]
29) The Earth, the Moon, and the Sun are aligned on the same plane as shown below. If the
Moon has a mass of 7.35 x 10 22 kg and the Sun has a mass of 1.99 x 10 30 kg, determine
the net gravitational force exerted by both the Moon and the Sun on Earth.
[3.51 x 10 22 N towards the Sun]
Moon
Earth
3.84 x 10 8 m
Sun
1.50 x 10 11 m
30) On the surface of Planet Magnus, which has a mass of 4.83 x 10 24 kg, an object has a
weight of 50.0 N and a mass of 30.0 kg. What is the radius of this planet?
[1.39 x 10 7 m]
31) What is the weight of a 20.0 kg object on the surface of the moon? The mass of the
moon is 7.34 x 10 22 kg and the radius of the moon is 1.74 x 10 6 m.
[32.3 N (down)]
32) An 80.0 kg astronaut is leaving the surface of the moon. The acceleration of the rocket is
12.8 m/s 2 [up]. On the moon, the gravitational acceleration is 1.62 m/s 2 [down].
Calculate the magnitude of the true weight and apparent weight of the astronaut.
[True weight is 130 N, apparent weight is 1.15 x 10 3 N]
33) How much does a stone with a mass of 0.100 kg weigh if it is 4.00 x 10 6 m above the
surface of the Earth?
[0.371 N]