CHAPTER 5 BLM ANSWER KEY
BLM 5-1: Vector Components/Skill BuilderAnswers
1. The vectors are non-perpendicular because the angle between them is 110.0º.
2. First, and are decomposed into the vertical and horizontal components. Second, the vertical components of and are added algebraically, and then the horizontal components of and are added algebraically. Third, the sum of the horizontal components and the sum of the vertical components are added by vector addition, using the Pythagorean theorem, to find the resultant vector for adding and .
3. A2x is negative because it points to the left.
4.
5.
6. A1x = cos 10º, A1y = sin 10º
7. A2x = cos 120º, A2y = sin 120º
8.
9.
10. = 12 km at 49º
BLM 5-2: Newton’s First and Third Laws/Skill Builder
Answers
1. – Newton’s First Law
(a) In a rear-end collision, as the car and the driver’s body are pushed forward, the driver’s head would jerk backward relative to the body, due to inertia. Headrests prevent this from happening, and thus prevent severe whiplash.
(b) A centrifuge is a spinning device that separates the solid and liquid parts of a substance. Due to inertia, the more massive solid parts sink to the bottom and the liquid parts remain on the top, as they have less resistance to being spun around. / (c) The tendency to remain in a straight line (inertia) is what keeps people from falling out of their seats when they are turned upside on a roller coaster loop.
– Newton’s Third Law
(a) Earth pulls on the Moon and the Moon pulls on Earth. The world’s oceans flow toward the Moon in response to its pull, creating a tide on the side of Earth facing the Moon. On the side of Earth facing away from the Moon, the oceans also flow outward, causing a tide, but this time it is because of the ocean’s inertia or resistance to rotating with Earth.
(b) Exhaust gases from burning fuel are pushed backward at a high speed by the rocket. The gases react by pushing the rocket forward. In essence, a rocket accelerates in one direction, while throwing mass in the opposite direction.
(c) The person’s feet push backward on the ground and the ground pushes forward on the person’s feet, moving the person forward. Walking is difficult on waxed floors and on ice because the coefficient of friction of these surfaces is below 0.2. This means that on these surfaces, a person cannot exert much force on the ground and the ground cannot exert much force of friction on the person.
2. (a) Acceleration of the squid
Average force on the squid
The average force on the squid is 75 N[up].
CHAPTER 5 BLM ANSWER KEY
(b) By Newton’s third law, force on the ejected mass is 75 N[down].The ejected mass of water is accelerated down at 42 m/s2.
BLM 5-3: Newton’s Third Law: Interaction Pairs/Skill Builder
Answers
1. The three agents are the hand, the bowling ball,
and Earth.
2. is the force that the hand is exerting upward on the bowling ball.
is the force that the bowling ball is exerting downward on the hand.
is the gravitational force that Earth is exerting downward on the bowling ball.
is the gravitational force that the bowling ball is exerting upward on Earth.
3. =
=
>
4. and ; and . They are interaction pairs because they are of equal magnitude and in opposite directions, and within each pair, the forces are exerted on two different objects. / 5. acts on the hand, acts on Earth, and both and act on the bowling ball.
6. The bowling ball will accelerate upward because the net force on it is upward; that is, is less than .
7. The movement of the ball is due to the unbalanced forces on it, not due to the balanced force of interaction pairs that acts on different objects.
8. The bowling ball would accelerate downward if the net force was downward; that is, if was less than .
BLM 5-4: Forces on an Inclined Plane/
Skill Builder
Answers
1. The process is called “vector decomposition.”
2. is a single force vector acting at an angle θ with the horizontal. Fx = cos θ is its horizontal component and Fy = sin θ is its vertical component such that the relationship holds.
3. The arrow for Fx would point to the left, the arrow for Fy would be unchanged, and the arrow for would lie between Fx and Fy.
4. Since , .
5. Fy would increase and Fx would decrease.
6. Earth’s gravity causes , which is the weight of the box. The vector points downward because gravity acts toward Earth’s centre.
7. Fgx would decrease and Fgy would increase.
8. Fgy = cos
9. Fgx = sin
10. The inclined plane exerts a normal force,, on the box, which is equal in magnitude to Fgy and acts perpendicular to the surface of the inclined plane in the positive y direction.
CHAPTER 5 BLM ANSWER KEY
BLM 5-5: Newton’s Laws: Problems/Problem SolvingAnswers
1. (a) Find the weight of the sign.
Each cable supports half the weight of the sign. The tension in each cable is given by the following equation.
Each cable has a tension of 1741 N.
(b) Again, each cable supports half the weight.
In this case, the tension in each cable is much higher: 8438 N. / 2. Refer to the free body diagram below. Select the x-axis and y-axis at right angles to the incline.
Vector / x-component (N) / y-component (N)
/ –851.28 / –1014.51
/ 253.63 / 0.0
/ 0.0 / –1014.51
/ –597.65 / 0.0
CHAPTER 5 BLM ANSWER KEY
(a) The net force on the block is 598 N down the inclined plane.(b)
The block’s acceleration is 4.4 m/s2 down the inclined plane.
3. Draw a free body diagram for each section of the train.
For car C
For car B
For car A
/ (a) The acceleration of the train is 1.31 m/s2[E].
(b)
The tension between the first and second cars is 33 440 N.
(c)
The tension between the second and third cars is 16 720 N.
4. Refer to the vector diagrams and the calculations below.
/
CHAPTER 5 BLM ANSWER KEY
(a)
Vector / x-component (N) / y-component (N)/ 55.0 / 95.26
/ 0.0 / –40.0
/ 44.55 / –22.70
/ 99.55 / 32.56
The net force on the object is 104.7 N[E18ºN].
The acceleration of the object is 2.6 m/s2[E18ºN].
(b)
The velocity of the object after 7.0 s is 18.3 m/s[E18ºN].
5. Refer to the free body diagram and calculations below.
CHAPTER 5 BLM ANSWER KEY
Along the horizontalThe child pulls on the handle with a force of 65.8 N at an angle of 30º to the horizontal.
BLM 5-6: Impulse and Momentum in Sports/
Science Inquiry
Answers
Part 1
Hockey might be selected as a favourite sport, and the responses could be as follows.
1. (a) A long impulse time would be required in slowly passing the puck to another player.
(b) A fast slapshot would require a short impulse time.
(c) A hard wrist shot would require a large impulse force, as would bodychecking an opposing player into the boards.
(d) A small impulse force could be the result of deflecting the puck by tapping it toward the net. / 2. (a) A goalie catches a puck by extending an arm and glove forward so that there will be plenty of room for the arm to move backward to make contact with the puck. This extends the time of the impact, thereby reducing the impact’s force. Players gain momentum by pushing off with their skates
and gaining speed before checking an opposing player, thus increasing the force of the impulse
on their opponent.
(b) Equipment required for hockey would be a puck, hockey sticks, skates, helmets, face masks, mouth guards, and all types of padding, such as shin pads, knee pads, shoulder pads, and goalie pads. Protective equipment such as padding increases the time of impact, reducing the force of impact.
Part 2
It is a very challenging task to invent a sports game or sporting event that is different from currently played games. The main requirement is that the student must describe how the players and their equipment make use of impulse and momentum principles to play the new game.
BLM 5-7: Chapter 5 Test/Assessment
Answers
1. first
2. second
3. an equal
4. the net force acting on it is zero
5. terminal velocity
6. N•s
7. impulse
8. The net force is acting upward.
9.
/
CHAPTER 5 BLM ANSWER KEY
10. As the elevator slows to a stop, your acceleration is downward, so the net force on you is downward: Since is negative, is negative or downward. The net force on you is the sum of the gravitational force acting downward and the normal force of the elevator acting upward: ; therefore, . Since the normal force is less than the gravitational force and the normal force is your apparent weight, your apparent weight would decrease.11. The force exerted by your arm muscles and the force exerted by the rope are forces acting on your hand.
12. (a)
(b) There is no net force on the boat, because it has neither vertical nor horizontal acceleration.
(c) Action-reaction pairs are forces that act on different objects and have equal magnitudes but opposite directions. The drawing shows an action-reaction pair: The woman pulls the boat with the same force with which the boat pulls her.
13.
Since the cable is exerting an upward force on the elevator, the elevator is exerting a downward force of 1.1 ´ 104 N on the cable. / 14. (a) Fg = mg
The mass of the rocket is 2.0 × 106 kg.
(b)
The acceleration of the rocket is 2.5 m/s2[upward].
(c)
The rocket reaches a velocity of
4.2 × 103 m/s[upward].
15. (a)
It takes the flare 4.59 s to reach its highest point. /
CHAPTER 5 BLM ANSWER KEY
(b)The flare rises to 1.03 × 102 m above ground.
16. (a)
The acorn is in the air for 1.28 s.
(b)
The acorn’s velocity is 12.5 m/s[downward] when it reaches the ground. / 17.
The average force of the racquet on the ball was
1.9 ´ 102 N.
18. Cars are made with bumpers that retract during a collision in order to increase the time of the collision, thus reducing the force of the impact. /