Download 03BC VA-Kinem-Fall-Newt WS08

Honors Physics
Velocity, Acceleration, Kinematics, Freely Falling Bodies, Newton’s Laws
Worksheet- Sec 3.6 to 3.10
Use g= 9.80 m /s2 as needed.
1. A ball is thrown straight upward. It slows down, comes to rest, speeds up and then strikes the
ground. While the ball is in the air, its acceleration (increases, decreases, remains the same).
(Answer: remains the same)
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2. As the mass of an object increases, its acceleration due to gravity (increases, decreases,
remains the same).
(Answer: remains the same)
3. A ball is thrown straight upward with a speed of 20 m/s. With what speed does the ball strike
the ground?
(Answer: 20 m/s)
4. A ball is thrown vertically upward with an initial velocity of 49 m/s.
(a) Sketch the ball’s acceleration vs. time graph.
(b) Sketch the ball’s velocity vs. time graph.
(c) Sketch the ball’s position vs. time graph.
Answers:
acceleration (m /s 2 )
(a)
0
10
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−9.8
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velocity (m/s)
(b)
height (m)
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€
€
€
€ (c)
50
40
30
20
10
0
−10
−20
−30
−40
−50
1
2
3
4
1
2
3
4
5
6
7
8
9
10
11
5 6
time (s)
7
8
9
10
11
130
120
110
100
90
80
70
60
50
40
30
20
10
time (s)
5. A ball is thrown vertically upward with an initial velocity of 58.8 m/s at t= 0.
(a) How long does the ball take to reach its maximum height? (Answer: 6.00 s)
(b) What is the ball’s maximum height? (Answer: 176 m)
(c) How long does the ball remain in the air? (Answer: 12.0 s)
(d) With what speed does the ball hit the ground? (Answer: 58.8 m/s)
(e) At what two times the the ball have a speed of 40.0 m/s? (Answer: 1.92 s, 10.1 s)
(f) At what two times is the height of the ball 100 m? (Answer: 2.05 s, 9.95 s)
(g) What is the height of the ball at t= 8.00 s? (Answer: 157 m)
(h) What is the velocity of the ball at t= 8.00 s? (Answer: −19.6 m/s)
(i) How far does the ball fall from t= 8.00 s to t= 9.00 s? (Answer: 24.5 m)
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6. A car whose initial velocity is 25 m/s is accelerated uniformly at the rate of 2.2 m /s2 for 4.5 s.
€ 35 m/s)
(a) What is the final velocity of the car? (Answer:
(b) What is the displacement of the car during the 4.5 s? (Answer: 130 m)
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7. A plane travels a distance of 6.0 x 10 2 m while being accelerated uniformly
from rest at the rate
2
of 4.5 m /s .
2
(a) How long does the plane take to travel the 6.0 x 10 m? (Answer: 16 s)
(b) What is the final speed of the plane? (Answer: 73 m/s)
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8. A bullet leaves the barrel of a rifle with an instantaneous speed of 550 m/s. The barrel of the
rifle is .80 m long.
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(a) What is the acceleration of the bullet while it is in the barrel of the rifle?
5
2
(Answer: 1.9 x 10 m /s )
−3
(b) For how long is the bullet in the barrel? (Answer: 2.9 x 10 s)
2
9. A car slows down for 7.5 s at the constant rate of −8.0 m /s while coming to a stop.
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(a) What was the initial velocity of the car? (Answer: 60 m/s)
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(b) How far did the car travel while it was slowing
down? (Answer: 230 m)
€ what effects on a body?
10. A force is a physical quantity that may have
(Answer: A force may change the speed or direction
of motion of a body. [Both the speed and
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direction of motion can be changed by a force.] )
11. Force is a (scalar, vector) quantity.
(Answer: vector)
12. A student claims that motion is not possible because all forces come in pairs that are equal in
magnitude but opposite in direction. This line of reasoning is incorrect because Newton’s
Third Law of Motion involves
(a) (one, two) objects and
(Answer: two)
(b) (one, two) forces
(Answer: two)
13. The total time a ball remains in the air is 14 s.
(a) With what speed was the ball thrown upward? (Answer: 69 m/s)
(b) What is the maximum height reached by the ball? (Answer: 240 m)
14. A car starts from rest and covers .85 km with the accelerator floored. The final velocity of the
car is 120 km/h.
2
2
(a) What is the car’s acceleration in m /s ? (Answer: .65 m /s )
(b) A position vs. time graph of the car’s motion would have what shape? (Answer: parabola)
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15. A ball rolls down an incline 60 m long. Its initial velocity is 10 m/s. The ball reaches the
bottom of the incline in 4.0 s.
(a) Find the ball’s acceleration. (Answer: 2.5 m /s2 )
(b) Find the speed of the ball when it reaches the bottom of the incline. (Answer: 20 m/s)
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16. A race car’s initial velocity is 44 m/s. The car slows down at a constant rate to a velocity of
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33 m/s over an 11 s interval.
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(a) What is the car’s acceleration? (Answer: −1.0 m /s2 )
(b) What is the car’s displacement during the interval? (Answer: 420 m)
17. An object travels on a straight line and its acceleration is negative. Take right as the positive
direction.
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(a) The object’s speed (must increase, may increase, may not increase).
(Answer: may increase)
(b) The object’s velocity (must decrease, may decrease, may not decrease).
(Answer: must decrease)
18. A stone is dropped from a tower 150 m high. The stone’s initial velocity is zero.
(a) With what speed does the stone strike the ground? (Answer: 54 m/s)
(b) How long is the stone in the air? (Answer: 5.5 s)
(c) Sketch a position vs. time graph for the stone.
Answer:
200
height (m)
150
100
50
0
1
2 3 4
time (s)
5
6
19. A 15 kg object is taken to planet X, where the acceleration due to gravity is 3.0 times what it is
on Earth. What is the object’s mass on planet X? (Answer: 15 kg)
20. A rocket accelerates from rest at 8.00 m /s2 for 60.0 s. The engine is then shut off.
(a) What is the rocket’s height when the engine is shut off? (Answer: 14400 m)
(b) What is the rocket’s velocity when the engine is shut off? (Answer: 480 m/s)
(c) What is the rocket’s maximum height? (Answer: 26200 m)
€ is shut off does the rocket strike the ground? (Answer: 122 s)
(d) How long after the engine
(e) With what speed does the rocket strike the ground? (Answer: 716 m/s)
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21. A body moves in a circle at constant speed.
(a) Explain why the body’s acceleration is not zero.
(b) According to Newton’s ____ Law of Motion, a force must act on the body to maintain its
circular motion.
Answers:
Δv
(a) a =
. Since velocity is a vector, its value changes when the direction of motion changes.
Δt
Because there is a change in velocity, there is also an acceleration.
(b) Second
€ 22. A force of 36 N causes an object to accelerate horizontally at 6.0 m /s2 on a frictionless
surface.. What is the weight of the object? (Answer: 59 N)
23. In each of the following situations, does Newton’s First Law of Motion best explain the motion
of the object?
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(a) A stone is dropped from a bridge.
(b) A stack of books sits on a desk.
(c) A rocket is traveling at 100000 km/h in deep space. The rocket is coasting at constant
speed.
(d) A stone is tied to one end of a string and is swung in a horizontal circle. The stone moves
at constant speed.
(e) Contestants pull on a rope in a tug of war. One group pulls on the rope with a force of
6000 N, north and the other group pulls on the rope with a force of 6000 N, south. The
rope does not move.
(f) An object sliding on the floor slowly comes to rest.
(Answer: Newton’s First Law explains the motion in these situations: (b), (c), (e) )
24. Newton’s First Law of Motion is associated closely with what property of matter?
(Answer: inertia)
25. (a) If no net force acts on a moving object then what is the shape of its trajectory?
(Answer: a straight line)
(b) If no net force acts on a moving object then its speed (increases, decreases, remains the
same). (Answer: remains the same)
26. Consider the velocity vs. time graph of an object’s motion.
velocity
B
A
C
D
time
List the intervals (A, B, C, D or none of these) that fit each description.
(a) A constant non-zero force acts on the object. (Answer: A, D)
(b) No net force acts on the object. (Answer: C)
(c) The object is moving in the negative direction. (Answer: none of these)
(d) A variable force acts on the object. (Answer: B)
(e) A force pointing in the positive direction acts on the object. (Answer: A)
(f) A constant negative force acts on the object. (Answer: D)
27. A ball takes 3.6 s to reach its maximum height. If the ball returns to its original height then
how long does the ball remain in the air? (Answer: 7.2 s)
28. The brakes of a 550 kg elevator produce an upward force of 4800 N. What is the acceleration
of the elevator? (Answer: −1.1 m /s2 )
29. Use Newton’s Second Law of Motion to prove that m(v F − v I ) = FNET Δt for a uniformly
accelerating object. This equation is known as the Impulse-Momentum equation.
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Answer:
F NET = ma
a=
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Δv
v − vI
= F
Δt
Δt
 v − vI 
So, F NET = m F
 ⇒ m(v F − v I ) = FNET Δt
 Δt 
30. An object of mass m accelerates at the rate a when net force F acts on the object. What would
1
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be
the
acceleration
of
an
object
whose
mass
is
m when net force 2F is applied?
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3
(Answer: 6 a)
31. An upward force of 70 N is applied to a 20 N ball. Find the acceleration of the ball.
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(Answer: 25 m /s2 )
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32. State which of Newton’s Laws of Motion is most closely associated with each of the following.
(a) action-reaction (Answer: Third Law)
(b) When a car makes a sudden stop, seatbelts are needed to protect passengers.
(Answer: First Law)
(c) When you step off a boat and onto a dock, the boat tends to move away from the dock.
(Answer: Third Law)
(d) F= ma (Answer: Second Law)
(e) When hot gases are ejected toward the ground from a rocket’s engine, the rocket
accelerates upward. (Answer: Third Law)
(f) Once a rocket leaves Earth’s orbit, it can travel at high speed for great distances without
using any fuel. (Answer: First Law)
(g) When acceleration is plotted as a function of mass for a constant force, the result is a
hyperbola. (Answer: Second Law)
(h) When a paper towel is slowly pulled, the towel remains attached to the roll. When the
towel is pulled quickly, it separates from the roll. (Answer: First Law)
33. A pitcher exerts a constant force on a .12 kg ball through a distance of 2.8 m. The ball leaves
the pitcher’s hand with a velocity of 42 m/s. What force does the pitcher exert on the ball?
(Answer: 38 N)
34. An object is accelerated by a 16.0 N force that acts in the direction the object is moving. The
object travels 58.7 m during the 3.40 s the force is applied. The velocity of the object at the end
of the 3.40 s interval is 22.5 m/s. What is the mass of the object? (Answer: 5.20 kg)
35. Consider the pulley system shown below.
(a) Find the magnitude of the downward acceleration
of the 20.0 kg mass. (Answer: 1.09 m /s2 )
(b) Find the tension in the rope. (Answer: 174 N)
(c) The masses are released from rest. Find the
speed of the 20.0 kg mass after 3.00 s.
(Answer: 3.27 m/s)
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16.0 kg
20.0 kg
36. Consider the pulley system shown below.
ML
M L = 16.0 kg
M R = 20.0 kg
MR
Mass M L slides on a horizontal
frictionless surface.
(a) Find the magnitude of the downward acceleration of the 20.0 kg mass.
(Answer: 5.44 m /s2 )
(b) Find the tension in the rope. (Answer: 87.0 N or 87.1 N)
37. What force is required to accelerate a 360 N object at 4.5 m /s2 on a horizontal, frictionless
surface? €(Answer: 170 N)
HOMEWORK
GUIDE
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Section in the
Notes
Worksheet Problems
3.6
6, 7, 8, 9, 14, 15, 16, 17
3.7
1, 2, 3, 4, 5, 13, 18, 20, 27
3.8
10, 11, 23, 24, 25
3.9
19, 21, 22, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37
3.10
12, 32