Download Dynamics Problems Set Newton`s Laws: 1. An elevator and its

Dynamics Problems Set
Newton's Laws:
1. An elevator and its contents have a combined mass of 6500 kg. It is suspended by a single cable.
(a)
Draw a free-body diagram of the elevator.
(b)
What force must the cable exert on the elevator when it is at rest?
(c)
What force must the cable exert on the elevator when it is moving upward at 2.0 m/s2?
(d)
What force must the cable exert on the elevator when it is moving downward at 2.0 m/s?
(e)
What force must the cable exert on the elevator when it is moving downward at 2.0 m/s2?
(f)
If the cable snapped, draw a new free-body diagram and determine the acceleration of the
elevator.
2. A model rocket of mass 4.80 x 102 g accelerates vertically upward at 34.0 m/s2 during launch,
overcoming both gravity and air resistance.
(a)
Draw a free-body diagram of the rocket once it has left the launch pad.
(b)
Calculate the thrust force applied by the rocket engine during launch if the air resistance acting
on the rocket is 2.40 N.
3. A rocket of mass 8400 kg is fired directly upward.
(a)
What upward force must be supplied by its engine if the rocket is to accelerate at 3.8 m/s2?
(Include a free-body diagram.)
(b)
If the engines suddenly stopped functioning, draw a new free-body diagram and determine the
acceleration of the rocket.
Newton's Laws and Kinematics:
4. A person throws a 2.4 kg object vertically upward and it reaches a maximum position 4.1 m above
the point of release.
(a)
What speed must the object have had upon release? Include a free-body diagram of the object
after release.
(b)
If the process of throwing the object vertically from rest took 0.823 s until it was released, what
was the acceleration of the object?
(c)
What force must the person have exerted during the throw to reach the determined height?
Provide a new free-body diagram of the object before release.
5. A bowling ball of mass 2.0 kg strikes a stationary pin of mass 5.00 x 102 g. The collision lasts for
0.45 s after which the pin moves off with a velocity of 12.8 m/s [W]. Calculate
(a)
the acceleration of the pin during the collision
(b)
the force exerted by the bowling ball on the pin (include a free-body diagram).
(c)
the acceleration of the bowling ball during the collision
Summing Forces:
6. If a 7.2 N force is required to accelerate a 3.4-kg object along a horizontal surface at a rate of 1.6
m/s2, what is the frictional resistance that is acting?
7. A wagon of mass 2.4 kg is pushed along the ground at 1.2 m/s2 [→] against a frictional force of 1.22
N. What is the applied force that is acting? Draw a free-body diagram.
8. Two monkeys of mass 34 kg and 42 kg each are hanging onto a 0.50 kg banana suspended by a vine
from a tree. A leaf falls on one of the monkeys and the vine snaps.
a)
Draw a free-body diagram of the banana.
b)
Determine the tension force of the vine before it snapped.
9. If 6.8 N of force are exerted horizontally on a 1.1-kg object and 2.4 N of friction are impeding its
slide, what is the object's acceleration?
Friction:
10. An applied force of 6.2 N [→] acts on a 2.1 kg object, pushing it horizontally across a surface
where the coefficient of kinetic friction is 0.15.
(a)
Determine the frictional force acting (include a free-body diagram).
(b)
Determine the object's acceleration.
11. A force of 1.2 N is applied to an object of mass 1.5 kg. It accelerates at 0.50 m/s2 [←] along a
surface. Determine the force of friction that is acting and the coefficient of kinetic friction involved.
12. Two children pull a toy truck of mass 2.4 kg along a rough horizontal surface. One child pulls with
a force of 8.4 N [N] and the other pulls with a force of 3.6 N [S]. The coefficient of friction between the
toy and surface is 0.18. What is the acceleration of the toy?
13. How much force would be required to start a 1.0-kg object sliding along a horizontal surface if the
coefficient of static friction is 0.20?
14. Show that an applied force of 4.0 N is insufficient to get a stationary 2.0-kg object to move
horizontally if the coefficient of starting friction is 0.25.
Friction and Kinematics:
15. A hockey puck of mass 200 g slides along the ice with a speed of 1.2 m/s when it reaches a rough
section where the coefficient of kinetic friction is 0.25. How long will it take the puck to stop sliding?
Include a free-body diagram. (Assume 2 significant digits.)
16. An object of mass 3.8 kg is pushed directly from rest along a horizontal surface, a distance of 1.2
m, and reaches a speed of 2.6 m/s by the end of the push. The frictional force acting is 6.7 N.
(a)
Determine the acceleration of the object while being pushed.
(b)
Determine the value of the applied force that is acting.
17. A stationary box of mass 4.2 kg is given a push of 8.2 N [S] along a surface where the frictional
force acting is 5.8 N [N]. The push lasts for 3.6 s and then the box is allowed to slide on its own until it
comes to rest.
(a)
Draw free-body diagrams to show the box being pushed and sliding on its own.
(b)
Determine the acceleration of the box as it is being pushed.
(c)
Calculate the speed of the box just as the push ceases.
(d)
Determine the acceleration of the box as it is sliding on its own and the time it takes to come to
rest.
Universal Gravitation:
18. An object of mass 40.0 kg rests on the surface of a planet with a mass of 8.2 x1022 kg and radius 3.6
x105 m.
(a)
Calculate the force of gravity acting on the object.
(b)
Determine the gravitational field strength "g" at the planet's surface.
(c)
Calculate the force of gravity acting on the object if it is placed at a position 6.4 x105 m above
the planet's surface.
19. An object of mass 50.0 kg rests at the surface of a planet with a mass of 6.2 x 1020 kg and a radius
of 3.8 x 104 m. What would the object weigh at an altitude equivalent to the planet's radius?
20. The gravitational field strength on the surface of Mars is 3.7 N/kg.
(a)
What would a person weigh on Mars if this person weighs 637 N on Earth?
(b)
What is the mass of Mars if its radius is 3.4 x 106 m?
21. The gravitational field strength on the surface of the Moon is 1.6 N/kg. The radius of the Moon is
1.7 x106 m.
(a)
How much would a 60.0-kg astronaut weigh in orbit around the Moon at an altitude of 2.0 x102
km above the lunar surface?
(b)
If an object is thrown vertically upward from the lunar surface with a speed of 10 m/s, what
maximum height will it reach?
22. A person stands on a set of bathroom scales which have been calibrated in Newtons. The scales read
500 N. (Assume three significant digits.)
(a)
What would the reading be if the same person stood on the scales on a planet where the
gravitational field strength, g, is 14 N/kg?
(b)
If this planet had a mass of 7.0 x1024 kg, what would its radius be?
(c)
What would this person weigh at an altitude of 2.8 x106 m above the planet's surface?
23. A 3.0-kg object is dropped from 4.0 m above the lunar surface and reaches the ground 2.24 s later.
(a)
What is the value of the force of gravity exerted by the Moon on the object?
(b)
If both the Moon's mass and radius were doubled, how long would it take the object to reach the
surface if dropped from the same height?
Answers:
1. b) 6.4x104 N []
c) 7.7x104 N []
d) 6.4x104 N []
e) 51 N []
2. b) 27.9 N []
3. a) 1.1x105 N []
b) 9.81 m/s2 []
4. a) 9.0 m/s []
b) 11 m/s2 []
c) 5.0 x101 N []
5. a) 28 m/s2 [W]
b) 14 N [W]
c) 5.0 m/s2 [E]
14. show it yourself!
15. 0.49 s
16. a) 2.8 m/s2 [→]
b) 17 N [→]
17. b) 0.57 m/s2 [S]
c) 2.1 m/s [S]
d) 1.38 m/s2 [←], 1.52 s
**All directions of the following vectors are
assumed to be towards the centre of
mass of the ‘attracting’ object, unless
otherwise stated
6. 1.8 N [backwards]
18. a) 1700 N
b) 42.2 N/kg
c) 220 N
7. 4.1 N [→]
19. 360 N
8. 750 N []
9. 4.0 m/s2 [fwd]
10. a) 3.1 N [← ]
b) 1.5 m/s2 [→]
11. Ff = 0.45 N [→], µ = 0.03
12. 0.23 m/s2 [N]
13. 2.0 N [→]
20. a) 240 N
b) 6.4 x1023 kg
21. a) 77 N
b) 31 m [] (moon), 5.1 m [] (earth)
22. a) 710 N
b) 5.8 x106 m
c) 320 N
23. a) 4.8 N
b) 3.2 s