SPH4U1. Name: Dynamics Unit Test ... ____ 2. The sum of all the forces acting
on a stationary object is the same as that acting on an object in uniform motion.
SPH4U1
Name:
Dynamics Unit Test
K–
C–
T– /20
/20
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Modified True/False
Indicate whether the sentence or statement is true or false. If false, change the identified word or phrase to make the sentence or statement true.
(K)
____ 1. The normal force FN that acts on an object is not always equal in magnitude and opposite in
direction to the gravitational force FG that is acting on it. _________________________ ____ 2. The sum of all the forces acting on a stationary object is the same as that acting on an object in uniform motion. _________________________ ____ 3. A rock is tied to a string and whirled around in a circle that describes a vertical plane. The tension in the string is greatest at the bottom of the circle and least at the top. ______________________________ ____ 4. If Earth’s mass and radius were both one half their present values, the acceleration due to gravity on the surface of the Earth would be four times its present value. __________________________________ ____ 5. For the following quantities, these are considered to be vectors: displacement, acceleration. _________________________ ____ 6. An object is thrown vertically upward. At the top of its flight, when its velocity is momentarily zero, its acceleration is zero. _________________________ ____ 7. If air resistance is negligible, the acceleration of all projectiles is exactly the same. _________________________ ____ 8. Provided that a boat always points perpendicular to the current in a river, the time it takes the boat to cross is independent of the strength of the current. _______________________________ ____ 9. Friction always acts against an object’s motion relative to the contact surface. _________________________ ____ 10. For an object travelling with uniform circular motion, its instantaneous velocity is always directed toward the centre of the circle. ______________________________
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SPH4U1
Name:
Dynamics Unit Test Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
(K)
____ 11. Two masses, A and B, hang on opposite ends of a rope suspended over a pulley. The mass of A is greater than the mass of B. If FTA represents the force of tension exerted by the rope on
mass A and FTB represents the force of tension exerted by the rope on mass B, then which of the following statements concerning the forces of tension is true? a. c. e. b.
d.
____ 12. The diagram below shows a rock on the end of a string being whirled around in a circle in the horizontal plane. The motion is viewed from above and the stone is rotating clockwise. What are the directions associated with its instantaneous velocity and instantaneous acceleration, respectively? a. south, east b. east, west
c. d.
south, south west, west
e.
south, west
____ 13. The relationship between the gravitational force of attraction, FG, of two objects on one another and their separation distance r is best illustrated by which of the following graphs?
a. A b. B
c. d.
C D
e.
E
____ 14. Which of the following graphs does NOT depict uniform motion?
a. A and B b. C only
c. d.
D and E B and D
e.
A and E
____ 15. Two hikers set out from the same spot and arrive at the same destination but they take different routes. Which of the following quantities must be the same for both hikers? a. distance c. average velocity e. acceleration b. average speed d. displacement
SPH4U1
Name:
Dynamics Unit Test ____ 16. The free-body diagram of a block being pushed up a rough ramp is best represented by
a. A b. B
c. d.
C D
e.
E
____ 17. Which of the following situations would produce the greatest acceleration? a. A 1.0-N force acting west and a 2.0-N force acting east on a 1.0-kg object. b. A 3.0-N force acting west and a 5.0-N force acting east on a 2.0-kg object. c. A 8.0-N force acting west and a 5.0-N force acting east on a 3.0-kg object. d. A 8.0-N force acting west and a 12.0-N force acting east on a 4.0-kg object. e. A 1.0-N force acting west and a 9.0-N force acting east on a 5.0-kg object. ____ 18. With respect to Newton’s third law, the action and reaction forces a. being equal, imply a “balanced” force situation b. act on different objects c. are equal provided the object is at rest d. are equal provided the object is moving with uniform motion e. are equal provided the object is NOT at rest or moving with uniform motion ____ 19. With all other things being equal, had the value of the universal gravitational constant been twice its present value, your weight would be a. 4 times as great c. the same e. ¼ as great b. 2 times as great d. ½ as great ____ 20. Astronauts on board an orbiting space station appear to be “floating” because a. they are in the vacuum of space b. they are outside Earth’s gravitational influence c. the force of gravity acting on them has been reduced to an insignificant level /10 d. they have become truly “weightless” e. they are in free fall along with the space station itself
Equations & Constants Force & Motion
v2 v1 a t
2 2 v 2 v1 2ad
d v1 t ½ at 2
vog vom vmg Fy F sin
Fnet ma
d v 2 t ½ at 2
ac
4 2 r T2
Fg mg sin
Fx F cos
Fg mg v 2 v1 at Fg mg cos
Gm1m2 Fg r2 d v t ac
G 6.67 10 11 N m
v2 r
2
kg 2
SPH4U1
Name:
Dynamics Unit Test Short Answer 21. Describe a situation where an object is accelerating but its velocity is zero.
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Problem 22. Two blocks are connected by a “massless” string over a “frictionless” pulley as shown in the diagram. a) Determine the acceleration of the blocks.
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(C)
SPH4U1
Name:
Dynamics Unit Test b) Calculate the tension in the string.
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23. A baseball is hit by a bat and given a velocity of 40.0 m/s at an angle of 30.0 above the horizontal. The height of the ball above the ground upon impact is 1.0 m. (a) A fielder is 110.0 m from home plate when the ball is hit and the ball’s trajectory is directly at him. If he begins running at the moment the ball is hit and catches the ball when it is still 3.0 m above the ground, how long does he run before catching the ball?
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SPH4U1
Name:
Dynamics Unit Test (b) How fast (average speed) does he have to run in order to catch the ball?
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24. A satellite orbits Earth at an altitude of 325 km above the planet’s surface. What is its orbital period? Express your answer in minutes. (rE = 6.38 106 m, ME = 5.98 1024 kg)
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SPH4U1
Name:
Dynamics Unit Test Answer Section MODIFIED TRUE/FALSE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS:
T T T F, two times its present value T F, 9.8 m/s2 [down] T T T F, tangent the circle
REF: REF: REF: REF: REF: REF: REF: REF: REF: REF:
K/U K/U K/U K/U K/U K/U K/U K/U K/U K/U
MULTIPLE CHOICE 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS:
E E D C D E E B B E
REF: REF: REF: REF: REF: REF: REF: REF: REF: REF:
K/U K/U K/U K/U K/U K/U K/U K/U K/U K/U
SHORT ANSWER 21. ANS: This would occur at the instant when an object is reversing direction. For example, when an object is thrown vertically upward its acceleration during the entire trip is 9.8 m/s2 [down], including its acceleration at the peak of its flight when its velocity is momentarily zero. REF: C
SPH4U1
Name:
Dynamics Unit Test PROBLEM 22. ANS: (a) For the 0.80-kg mass: Free-body diagram:
FN acting up Fg acting down FT acting to the right (this is the positive direction) FK acting to the left (this is the negative direction)
0.80 kg(a) = FT – KFN 0.80 kg(a) = FT – 0.14(0.80 kg)(9.8 N/kg) 0.80 kg(a) = FT – 1.10 N For the 2.0-kg mass: Free-body diagram:
FN acting perpendicular to the ramp (upward) Fg acting down FT acting up along the ramp (this is the negative direction) FK acting up along the ramp
2.0 kg(a) = 2.0 kg(9.8 N/kg)(sin 30º) – FT – 0.14(2.0 kg)(9.8 N/kg)(cos 30º) 2.0 kg(a) = –FT + 7.42 N Solving the system of equations: a = 2.3 m/s2 The system will accelerate at 2.3 m/s2. (b) FT = 0.80 kg(a) + 1.10 N = 0.80 kg(2.26 m/s2) + 1.10 N FT = 2.9 N The tension in the string is 2.9 N. REF: T
SPH4U1
Name:
Dynamics Unit Test 23. ANS: (a) Time of flight: v1 = –40.0 m/s(sin 30.0º) = –20.0 m/s a = 9.8 m/s2 d = –2.0 m t = ? –2.0 = (–20.0)t + 4.9(t)2 Solving the quadratic: t = 0.10 s (way up) and 3.98 s (way down) The fielder must run for 4.0 s in order to catch the ball. (b) Horizontal range: d = vt = 40.0 m/s(cos 30)(3.98 s) = 138 m The fielder must run a distance of: 138 m – 110.0 m = 28 m. The speed of the fielder:
The fielder must run with an average speed of 7.0 m/s. REF: T 24. ANS: The orbital radius is 6.38 106 m + 3.25 105 m = 6.705 106 m The centripetal force acting on the satellite is supplied by gravity. FC = Fg
The orbital period is 91.0 min. REF: T
