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Name: ________________________ Class: ___________________ Date: __________
ID: A
Review
Problem
1.
(4 points)
F 1 is 57 N, of force ä
F 2 is 57 N, and of ä
F 3 is 57 N. The angles θ 1 and θ 2 are 30° each.
The magnitude of the force ä
ä
ä
F .
Use the graphical method to find the resultant of the forces F , F , and ä
1
2.
2
3
(4 points)
A has magnitude 58.0 units and is inclined to the positive axis of x at 42.0°. Vector ä
B has magnitude 36.0
A vector ä
ä
units and is inclined to the positive axis of x at 121°. Vector C has magnitude 40.0 units and is inclined to the
ä.
A, ä
B , and C
positive axis of x at 53.0°. Use the graphical method to find the resultant of the vectors ä
3.
(4 points)
A river flows at a speed of 4.60 m/s. A boat, capable of moving with a speed of 5.80 m/s in still water is rowed
across the river at an angle of 53.0° to the river flow. Calculate the resultant velocity with which the boat moves
and the angle that its resultant motion makes to the river flow.
4.
(4 points)
What should be the angle between two vectors of magnitudes 3.20 and 5.70 units, so that their resultant has a
magnitude of 6.10 units?
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Name: ________________________
5.
ID: A
(4 points)
An airplane has to fly eastward to a destination 856 km away. If wind is blowing at 18.0 m/s northward and the air
speed of the plane is 161 m/s, in what direction should the plane head to reach its destination?
6.
(4 points)
A 2.7-kg box is released on a horizontal surface with an initial speed of 2.9 m/s. It moves on the surface with a
deceleration of 0.27 m/s2. Calculate the kinetic friction force on the box.
7.
(4 points)
A block of 7.80 kg kept on an inclined plane just begins to slide at an angle of inclination of 35.0°. Once it has
been set into motion, the angle is reduced to 30.0° to keep the block moving at constant speed. Calculate the
maximum force of static friction and the force of kinetic friction for the surfaces in contact.
8.
(4 points)
The system shown below is in equilibrium. Calculate the force of friction acting on the block A. The mass of
block A is 4.10 kg and that of block B is 4.30 kg. The angle θ is 33.0°.
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ID: A
Review
Answer Section
PROBLEM
1. ANS:
Zero
0
PTS: 4
DIF: 3
REF: Page 120
OBJ: 5.1.1 Evaluate the sum of two or more vectors in two dimensions graphically.
NAT: B.4
TOP: Evaluate the sum of two or more vectors in two dimensions graphically.
KEY: Sum of vectors
MSC: 3
NOT: Draw the vectors to scale and use the protractor to draw them tip to tail. The closing side of the polygon in
reverse order is the resultant.
BNK: Chapter 5-Forces in Two Dimensions
2. ANS:
The resultant is 113 units at an angle of 64.4° to the positive axis of x.
PTS: 4
DIF: 3
REF: Page 120
OBJ: 5.1.1 Evaluate the sum of two or more vectors in two dimensions graphically.
NAT: B.4
TOP: Evaluate the sum of two or more vectors in two dimensions graphically.
KEY: Sum of vectors
MSC: 3
NOT: Draw the vectors to scale and use the protractor to draw them tip to tail. The closing side of the polygon in
reverse order is the resultant. Measure the length of the resultant to get the magnitude of the vector, and use a
protractor to find the direction of the resultant.
BNK: Chapter 5-Forces in Two Dimensions
3. ANS:
The boat moves with 9.32 m/s at 29.8° to the river flow.
PTS:
OBJ:
NAT:
KEY:
NOT:
BNK:
4. ANS:
98.7°
4
DIF: 3
REF: Page 122
5.1.3 Solve for the sum of two or more vectors by adding the components of the vectors.
B.4
TOP: Solve for the sum of two or more vectors by adding the components of the vectors.
Sum of vectors
MSC: 3
Resolve the velocity of the boat into components along and perpendicular to the river flow.
Chapter 5-Forces in Two Dimensions
PTS:
OBJ:
NAT:
KEY:
NOT:
BNK:
4
DIF: 3
REF: Page 122
5.1.3 Solve for the sum of two or more vectors by adding the components of the vectors.
B.4
TOP: Solve for the sum of two or more vectors by adding the components of the vectors.
Sum of vectors
MSC: 3
Resolve one of the vectors into components along and perpendicular to the second vector.
Chapter 5-Forces in Two Dimensions
1
ID: A
5. ANS:
6.42° south of east
PTS: 4
DIF: 3
REF: Page 122
OBJ: 5.1.3 Solve for the sum of two or more vectors by adding the components of the vectors.
NAT: B.4
TOP: Solve for the sum of two or more vectors by adding the components of the vectors.
KEY: Sum of vectors
MSC: 3
NOT: Resolve the velocity of the plane in and perpendicular to the direction of the wind.
BNK: Chapter 5-Forces in Two Dimensions
6. ANS:
0.73 N
PTS: 4
DIF: 2
REF: Page 127
OBJ: 5.2.1 Define the friction force.
NAT: B.4
TOP: Define the friction force.
KEY: Friction
MSC: 2
NOT: The only force on the box is the kinetic friction, which should be equal to the product of mass and
acceleration of the box.
BNK: Chapter 5-Forces in Two Dimensions
7. ANS:
The maximum force of static friction is 43.8 N and the force of kinetic friction is 38.2 N.
PTS: 4
DIF: 3
REF: Page 127
OBJ: 5.2.2 Distinguish between static and kinetic friction.
NAT: B.4
TOP: Distinguish between static and kinetic friction.
KEY: Inclined plane
MSC: 3
NOT: The maximum force of static friction is equal to the force that just moves a static object. The kinetic
friction force is equal to the force that keeps it moving at constant speed.
BNK: Chapter 5-Forces in Two Dimensions
8. ANS:
64.9 N
PTS: 4
DIF: 2
REF: Page 131
OBJ: 5.3.1 Determine the force that produces equilibrium when three forces act on an object.
NAT: B.4
TOP: Determine the force that produces equilibrium when three forces act on an object.
KEY: Equilibrant MSC: 3
NOT: The tension in the three strings keeps the knot in equilibrium. The tension in the horizontal string is equal
to the friction on the block A.
BNK: Chapter 5-Forces in Two Dimensions
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