Questions and Answers for Topic #06
Topic 6 Concepts and Skills
Vocabulary, Variables and Equations
|Topic #06 Concepts and Skills
Link to "Concepts and Skills"
|Topic 6 Vocabulary
Scalar (Quantity): A quantity that has only magnitude; it has a number and a unit, but has no statement of direction.
Vector (Quantity): A quantity that has both magnitude and direction; it has a number, a unit and a direction.
Displacement: The vector quantity that defines the distance and direction between two positions.
Velocity: The vector quantity that defines the speed and direction of a moving object. Descriptive adjectives such as instantaneous, constant and average may be used along with this term.
Acceleration: The vector quantity that defines the rate at which the speed of an object changes as well as the direction in which the change occurs. Descriptive adjectives such as instantaneous, constant and average may be used along with this term.
Force: A push or pull exerted on an object having magnitude and direction; it may be either a contact or long range force.
Graphical Representation: An arrow or arrow-tipped line segment that symbolizes a vector quantity with a specified length and direction.
Algebraic Representation: Representation of a vector with an italicized letter in bold face type, which is often used in printed materials; in handwritten materials the algebraic representation of a vector is accomplished by writing the appropriate variable symbol with a forward facing arrow drawn above it.
Resultant (Vector): The sum of two or more vectors.
Equilibrant (Vector): A single, additional force that is exerted on a an object to produce equilibrium, which has the same magnitude as the resultant force, but is opposite in direction.
Vector Resolution: The process of breaking a vector into its (x and y) components.
Vector Component: The x or y portion of a vector that has been broken into its components.
Vector Addition: The process of adding two or more vectors together;
this can be done graphically or algebraically. This is never as simple
a task as simple arithmetic addition except when the vectors are in the
same direction such as both are on the x-axis.
|Review Questions:Chapter 4
|Application Questions:Chapter 4
11. A vector drawn 15 mm long represents a velocity of 30 m/s. How long
should you draw a vector to represent a velocity of 20 m/s?
|Word Problems:Problem Set #6: Follow the written directions unless
indicated otherwise by your instructor.
GRAPHICAL SOLUTIONS: Solve these problems by carefully drawing the vector information described and measuring the final answer using a protractor and ruler. Check answers using Trig.
1. After walking 11 km due north from camp, a hiker then walks
11 km due east.
2. A plane flying due north at 1.00x10^2 m/s is blown due west at 5.0x10^1 m/s by a strong wind. Find the plane's resultant velocity.
3. A motorboat heads due east at 16 m/s across a river that flows
due south at 9.0 m/s.
4. While flying due west at 120 km/h, an airplane is blown due north at 45 km/h by the wind. What is the plane's resultant velocity?
5. A salesperson leaves the office and drives 26 km due north along a straight highway. A turn is made onto a highway that leads in a direction of 60.0 degrees. The driver continues on the highway for a distance of 62 km and then stops. What is the total displacement of the salesperson from the office?
6. Two soccer players kick the ball at exactly the some time. One player's foot exerts a force of 66 N north. The other's foot exerts a force of 88 N east. What is the magnitude and direction of the resultant force on the ball?
7. Two forces of 62 N each act concurrently on a point P.
Determine the magnitude of the resultant force acting on point P when the
angle between the forces is as follows:
8. In problem 7, what happens to the resultant of two forces as the angle between them increases?
9. A weather team releases a weather balloon. The balloon's buoyancy accelerates it straight up at 15 m/s^2. A wind accelerates it horizontally at 6.5 m/s^2. What is the magnitude and direction (with reference to the horizontal) of the resultant acceleration?
10. What is the vector sum of a 65 N force acting due east and a 32 N force acting due west?
11. A plane flies due north at 225 km/h. A wind blows it due east at 55 km/h. What is the magnitude and direction of the plane's resultant velocity?
12. A meteoroid passes between the moon and the earth. A gravitational force of 6.0x10^2 N pulls the meteoroid towards the moon. At the same time, a gravitational force of 4.8x10^2 N pulls it toward the earth. The angle between the two forces is 130.0 degrees. The moon's force acts perpendicularly to the meteoroids original path. What is the resultant magnitude and direction of the force acting on the meteoroid? State the direction in reference to the meteoroids original path.
MATHEMATICAL SOLUTION: Solve the following problems mathematically using trigonometry. Include a labeled sketch of each problem's vector information.
13. A 110 N force and a 55 N force act on point P. The 110 N force acts due north. The 55 N force acts due east. What is the magnitude and direction of the resultant force?
14. A motorboat travels at 8.5 m/s. It heads straight across
a river 110 m wide.
15. A boat heads directly across a river 41 m wide at 3.8 m/s.
The current is flowing at 2.2 m/s.
16. A 42 km/h wind blows in the direction 215 degrees. What is the resultant velocity of a plane that flies a heading of 125 degrees at 152 km/h?
17. Two 15 N forces act concurrently on point P. FInd the
magnitude of their resultant when the angle between them is
18. A boat travels at 3.8 m/s and heads straight across a river
240m wide. The river flows at 1.6 m/s.
19. Determine the magnitude of the resultant of a 4.0x10^-1 N
force and a 7.0x10^1 N force concurrently acting when the angle between
SOLVING FOR THE EQUILIBRANT: The equilibrant is a vector having exactly the same magnitude as the resultant vector, but is exactly 180o opposite the direction of the resultant.
20. A force of 55N acts due west on an object. What added single force on the object produces equilibrium?
21. Two forces act concurrently on a point P. One force
is 6.0x10^1 N due east. The second force is 8.0x10^1 N due north.
22. A 62N force acting at 30.0 degrees and a second 62N force
acting at a 60.0 degrees are concurrent forces.
23. A 23 N force acts at 225 degrees. A 48 N force acts at 315 degrees. The two forces act on the same point. What is the magnitude and direction of the equilibrant?
24. A 33 N force acting due north and a 44 N force acting at 30 degrees act concurrently on a point P. What is the magnitude and direction of a third force that produces equilibrium at point P?
RESOLVING A VECTOR INTO ITS COMPONENTS
25. A heavy box is pulled across a wooden floor with a rope.
The rope forms an angle of 60 degrees with the floor. A tension of
8.0x10^1 N is maintained on the rope. What force actually is pulling
the box across the floor?
26. An airplane flies at 301 degrees at 5.0x10^2 km/h. At
what rate is the plane moving?
27. By applying a force of 72 N along the handle of a lawnmower,
a student can push it across the lawn. Find the horizontal component
of this force when the handle is held at an angle with the lawn of
28. A house address sign is hung from a post with a lightweight rod as shown in figure 6-14. If the sign weighs 4.5 N, what is the force in the chain?
29. A water skier is towed by a speedboat. The skier moves to one side of the boat in such a way that the towrope forms an angle of 55 degrees with the wake of the boat. The tension on the rope is 350 N. What would be the tension on the rope if the skier were directly behind the boat?
GRAVITATIONAL FORCE AND INCLINED PLANES: Using trig. to find the normal force.
30. A 5.00x10^2 N trunk is placed on an inclined plane that forms
a 66 degree angle with the horizontal.
31. A car weighing 12000 N is parked on a 36 degree slope.
32. In order to slide a 325 N trunk up a 20.0 degree inclined plane at a constant speed, a force of 211 N is applied. What is the force of friction acting on the trunk?