Sections
Chapter Review

# Chapter Review

### Concept Items

#### 5.1Vector Addition and Subtraction: Graphical Methods

1.
There is a vector $A→$, with magnitude $5$ units pointing towards west and vector $B→$, with magnitude $3$ units, pointing towards south. Using vector addition, calculate the magnitude of the resultant vector.
1. 4.0
2. 5.8
3. 6.3
4. 8.0
2.
How can one find the resultant vector using the head-to-tail method?
1. By joining the head of the first vector to the head of the last.
2. By joining the head of the first vector with the tail of the last.
3. By joining the tail of the first vector to the head of the last.
4. By joining the tail of the first vector with the tail of the last.
3.
What is the global angle of $20∘$ south of west?
1. $110∘$
2. $160∘$
3. $200∘$
4. $290∘$

#### 5.2Vector Addition and Subtraction: Analytical Methods

4.
What is the angle between the x and y components of a vector?
1. $0∘$
2. $45∘$
3. $90∘$
4. $180∘$
5.
Two vectors are equal in magnitude and opposite in direction. What is the magnitude of their resultant vector?
1. The magnitude of the resultant vector will be zero.
2. The magnitude of resultant vector will be twice the magnitude of the original vector.
3. The magnitude of resultant vector will be same as magnitude of the original vector.
4. The magnitude of resultant vector will be half the magnitude of the original vector.
6.
How can we express the x and y-components of a vector in terms of its magnitude, $A$, and direction, global angle $θ$?
1. $Ax=Acos⁡θ$ $Ay=Asin⁡θ$
2. $Ax=Acos⁡θ$ $Ay=Acos⁡θ$
3. $Ax=Asin⁡θ$ $Ay=Acos⁡θ$
4. $Ax=Asin⁡θ$ $Ay=Asin⁡θ$
7.

True or False—Every 2-D vector can be expressed as the product of its x and y-components.

1. True
2. False

#### 5.3Projectile Motion

8.
Horizontal and vertical motions of a projectile are independent of each other. What is meant by this?
1. Any object in projectile motion falls at the same rate as an object in freefall, regardless of its horizontal velocity.
2. All objects in projectile motion fall at different rates, regardless of their initial horizontal velocities.
3. Any object in projectile motion falls at the same rate as its initial vertical velocity, regardless of its initial horizontal velocity.
4. All objects in projectile motion fall at different rates and the rate of fall of the object is independent of the initial velocity.
9.
Using the conventional choice for positive and negative axes described in the text, what is the y-component of the acceleration of an object experiencing projectile motion?
1. $−9.8m/s$
2. $−9.8m/s2$
3. $9.8m/s$
4. $9.8m/s2$

#### 5.4Inclined Planes

10.

True or False—Kinetic friction is less than the limiting static friction because once an object is moving, there are fewer points of contact, and the friction is reduced. For this reason, more force is needed to start moving an object than to keep it in motion.

1. True
2. False
11.
When there is no motion between objects, what is the relationship between the magnitude of the static friction $fs$ and the normal force $N$?
1. $fs≤N$
2. $fs≤μsN$
3. $fs≥N$
4. $fs≥μsN$
12.
What equation gives the magnitude of kinetic friction?
1. $fk=μsN$
2. $fk=μkN$
3. $fk≤μsN$
4. $fk≤μkN$

#### 5.5Simple Harmonic Motion

13.
Why is there a negative sign in the equation for Hooke’s law?
2. The negative sign indicates that the direction of the applied force is opposite to that of displacement.
3. The negative sign indicates that the direction of the restoring force is opposite to that of displacement.
4. The negative sign indicates that the force constant must be negative.
14.

With reference to simple harmonic motion, what is the equilibrium position?

1. The position where velocity is the minimum
2. The position where the displacement is maximum
3. The position where the restoring force is the maximum
4. The position where the object rests in the absence of force
15.
What is Hooke’s law?
1. Restoring force is directly proportional to the displacement from the mean position and acts in the the opposite direction of the displacement.
2. Restoring force is directly proportional to the displacement from the mean position and acts in the same direction as the displacement.
3. Restoring force is directly proportional to the square of the displacement from the mean position and acts in the opposite direction of the displacement.
4. Restoring force is directly proportional to the square of the displacement from the mean position and acts in the same direction as the displacement.

### Critical Thinking Items

#### 5.1Vector Addition and Subtraction: Graphical Methods

16.

True or False—A person is following a set of directions. He has to walk 2 km east and then 1 km north. He takes a wrong turn and walks in the opposite direction for the second leg of the trip. The magnitude of his total displacement will be the same as it would have been had he followed directions correctly.

1. True
2. False

#### 5.2Vector Addition and Subtraction: Analytical Methods

17.
What is the magnitude of a vector whose x-component is $2units$ and whose angle is $60∘$?
1. $1.0units$
2. $2.0units$
3. $2.3units$
4. $4.0units$
18.
Vectors $A→$ and $B→$ are equal in magnitude and opposite in direction. Does $A→−B→$ have the same direction as vector $A→$ or $B→$?
1. $A→$
2. $B→$

#### 5.3Projectile Motion

19.
Two identical items, object 1 and object 2, are dropped from the top of a $50.0m$ building. Object 1 is dropped with an initial velocity of $0m/s$, while object 2 is thrown straight downward with an initial velocity of $13.0m/s$. What is the difference in time, in seconds rounded to the nearest tenth, between when the two objects hit the ground?
1. Object 1 will hit the ground $3.2s$ after object 2.
2. Object 1 will hit the ground $2.1s$ after object 2.
3. Object 1 will hit the ground at the same time as object 2.
4. Object 1 will hit the ground $1.1s$ after object 2.
20.

An object is launched into the air. If the y-component of its acceleration is 9.8 m/s2, which direction is defined as positive?

1. Vertically upward in the coordinate system
2. Vertically downward in the coordinate system
3. Horizontally to the right side of the coordinate system
4. Horizontally to the left side of the coordinate system

#### 5.4Inclined Planes

21.
A box weighing $500N$ is at rest on the floor. A person pushes against it and it starts moving when $100N$ force is applied to it. What can be said about the coefficient of kinetic friction between the box and the floor?
1. $μk=0$
2. $μk=0.2$
3. $μk<0.2$
4. $μk>0.2$
22.
The component of the weight parallel to an inclined plane of an object resting on an incline that makes an angle of $70.0∘$ with the horizontal is $100.0N$. What is the object’s mass?
1. $10.9kg$
2. $29.8kg$
3. $106kg$
4. $292kg$

#### 5.5Simple Harmonic Motion

23.
Two springs are attached to two hooks. Spring A has a greater force constant than spring B. Equal weights are suspended from both. Which of the following statements is true?
1. Spring A will have more extension than spring B.
2. Spring B will have more extension than spring A.
3. Both springs will have equal extension.
4. Both springs are equally stiff.
24.
Two simple harmonic oscillators are constructed by attaching similar objects to two different springs. The force constant of the spring on the left is $5N/m$ and that of the spring on the right is $4N/m$. If the same force is applied to both, which of the following statements is true?
1. The spring on the left will oscillate faster than spring on the right.
2. The spring on the right will oscillate faster than the spring on the left.
3. Both the springs will oscillate at the same rate.
4. The rate of oscillation is independent of the force constant.

### Problems

#### 5.1Vector Addition and Subtraction: Graphical Methods

25.
A person attempts to cross a river in a straight line by navigating a boat at $15m/s$. If the river flows at $5.0m/s$ from his left to right, what would be the magnitude of the boat’s resultant velocity? In what direction would the boat go, relative to the straight line across it?
1. The resultant velocity of the boat will be $10.0m/s$. The boat will go toward his right at an angle of $26.6∘$ to a line drawn across the river.
2. The resultant velocity of the boat will be $10.0m/s$. The boat will go toward his left at an angle of $26.6∘$ to a line drawn across the river.
3. The resultant velocity of the boat will be $15.8m/s$. The boat will go toward his right at an angle of $18.4∘$ to a line drawn across the river.
4. The resultant velocity of the boat will be $15.8m/s$. The boat will go toward his left at an angle of $18.4∘$ to a line drawn across the river.
26.
A river flows in a direction from south west to north east at a velocity of $7.1m/s$. A boat captain wants to cross this river to reach a point on the opposite shore due east of the boat’s current position. The boat moves at $13m/s$. Which direction should it head towards if the resultant velocity is $19.74m/s$?
1. It should head in a direction $22.6∘$ east of south.
2. It should head in a direction $22.6∘$ south of east.
3. It should head in a direction $45.0∘$ east of south.
4. It should head in a direction $45.0∘$ south of east.

#### 5.2Vector Addition and Subtraction: Analytical Methods

27.
A person walks $10.0m$ north and then $2.00m$ east. Solving analytically, what is the resultant displacement of the person?
1. $|R→|=10.2m$, $θ=78.7∘$ east of north
2. $|R→|=10.2m$, $θ=78.7∘$ north of east
3. $|R→|=12.0m$, $θ=78.7∘$ east of north
4. $|R→|=12.00m$, $θ=78.7∘$ north of east
28.
A person walks $12.0∘$ north of west for $55.0m$ and $63.0∘$ south of west for $25.0m$. What is the magnitude of his displacement? Solve analytically.
1. $10.84m$
2. $65.1m$
3. $66.04m$
4. $80.00m$

#### 5.3Projectile Motion

29.
A water balloon cannon is fired at $30m/s$ at an angle of $50∘$ above the horizontal. How far away will it fall?
1. $2.35m$
2. $3.01m$
3. $70.35m$
4. $90.44m$
30.

A person wants to fire a water balloon cannon such that it hits a target 100 m away. If the cannon can only be launched at 45° above the horizontal, what should be the initial speed at which it is launched?

1. 31.3 m/s
2. 37.2 m/s
3. 980.0 m/s
4. 1,385.9 m/s

#### 5.4Inclined Planes

31.
A coin is sliding down an inclined plane at constant velocity. If the angle of the plane is $10∘$ to the horizontal, what is the coefficient of kinetic friction?
1. $μk=0$
2. $μk=0.18$
3. $μk=5.88$
4. $μk=∞$
32.

A skier with a mass of 55 kg is skiing down a snowy slope that has an incline of 30°. Find the coefficient of kinetic friction for the skier if friction is known to be 25 N .

1. $μk=0μk=0$
2. $μk=0.05μk=0.05$
3. $μk=0.09μk=0.09$
4. $μk=∞μk=∞$

#### 5.5Simple Harmonic Motion

33.
What is the time period of a $6cm$ long pendulum on earth?
1. $0.08s$
2. $0.49s$
3. $4.9s$
4. $80s$
34.
A simple harmonic oscillator has time period $4s$. If the mass of the system is $2kg$, what is the force constant of the spring used?
1. $0.125N/m$
2. $0.202N/m$
3. $0.81N/m$
4. $4.93N/m$