Quiz#1

Equations:

displacement = velocity * time

distance = speed * time

Fnet = m * a

1. While Dexter is on a camping trip with his boy scout troop, the scout leader gives each boy a compass and a map. Dexter's map contains several sets of directions. One of the directions in Dexter's set reads

Walk 4 km north and then walk 8 km at 30º south of west.

In the space below, utilize the scale of 1 cm = 1 km and the head-to-tail addition method in order to determine the resultant displacement for this set of directions. Label the magnitude of each vector. Place arrowheads on each vector. Clearly label the resultant, along with its magnitude and direction. Construct a clear and accurate diagram.

2. Rosa Bote is navigating the Mississippi. Her boat can travel straight across the river with a velocity of 8.0 m/sec, East. On Tuesday, the river current was 3.0 m/sec, South.

a. Use the Pythagorean theorem to determine the resultant velocity (both magnitude and direction) of the boat?

b. If the river is 120 meters wide, then how much time did it take Rosa to cross the river?

c. How far downstream will Rosa Bote be when she reaches the other side?

d. How much time will it take the boat to go shore to shore on Wednesday if the current velocity is 1.5 m/s, South? Support your answer with a calculation or explanation.

3. A pack of Arctic wolves discover the carcass of a dead bear. A tug-of-war ensues as four wolves begin pulling in different directions upon the carcass. A top view of the four horizontal forces are shown in the sketch (unscaled) to the right. Assume that the vertical (up and down) forces (Fgrav and Fnorm) cancel each other out.

a. Use some method of vector addition to determine the resultant (vector sum) of all four vectors. Clearly explain your work and show your calculations in the space below for full credit.

b. Determine the acceleration of the 200-kg carcass at the instant shown in the diagram above.

4. Kent Findhisway, a visitor to the school, meets you in the doorway of the physics classroom (Room 159) and wants directions to the Autos Courtyard. Being entrenched in the subject of vectors, you decide to describe the necessary movement using a series of displacement vectors. Using complete sentences, describe the necessary displacements (magnitude and direction) which will take Kent through the hallways to the Autos courtyard. Use the diagram below and the indicated scale (1 cm = 5.0 m).

Quiz#2

1. Consider the map of the United States below. Given the scale that 1 cm = 400 km, use a protractor and a ruler to determine the displacement for the following trips. Indicate both the magnitude and the direction for each displacement vector.

2. Aaron Agin is adding vectors for his homework assignment. In his hurry, he failed to identify the resultant. What was Aaron trying to add (A + B + C or B + A + D or ...) and which one of the vectors is the resultant? Answer each question clearly and give an explanation using complete sentences.

Aaron was trying to add __________.

The resultant is vector _________.

Explanation:

3. Choose a scale and draw an accurately drawn vector addition diagram to determine the resultant of the following two vectors. In your diagram:

a. clearly indicate the scale

b. place arrowheads upon all vectors

c. label the magnitude and direction of each vector

d. label the resultant as R.

Indicate the the magnitude and direction of the resultant.

4 m/s, 45 degrees + 3 m/s, 315 degrees

4. In the Vector Addition Lab, the following data was collected for determining the displacement from the door of the Physics classroom to location 21E. Anna Litical (that bright young lady who knows all the answers) decides to determine the resultant the quick way. She first simplified her data into a pair of east-west and north-south vectors and then used the Pythagorean Theorem to determine the resultant displacement from the physics classroom to her assigned location.

Use Anna's method to determine the resultant displacement.

Quiz#3

Equations:

1. Rosa Bote is navigating the Mississippi. Her boat can travel straight across the river with a velocity of 8.0 m/sec, East. On Tuesday, the river current was 3.0 m/sec, South.

a. Use the Pythagorean theorem to determine the resultant velocity (both magnitude and direction) of the boat?

b. If the river is 120 meters wide, then how much time did it take Rosa to cross the river?

c. How far downstream will Rosa Bote be when she reaches the other side?

d. How much time will it take the boat to go shore to shore on Wednesday if the current velocity is 1.5 m/s, South? Support your answer with a calculation or explanation.

2. An airplane leaves O'Hare and flies with an average velocity of 500 km/hr, 120-degrees towards a Canadian destination (see diagram at the right). Use trigonometric methods to determine the northward and westward components of the velocity vector. Show your work in the space provided.

vnorth =_____________

vwest = _____________

Show Calculations Here:

If the Canadian border is 1500 km due North of O'Hare, then how much time will elapse before the plane flies over the Canadian border? Show a clear calculation.

3. The trajectory (path) of a projectile is _____________________.

4. Li Ping Phar, the famous Chinese ski jumper, leaves the ramp with an initial velocity of 34.9 m/s at an angle of 35 degrees. Assume that the skier lands at the same height as the top of the ramp and that the skier is a projectile. Use trigonometric functions, kinematic equations, and an understanding of projectile motion to answer the following questions.

a. Determine the horizontal and vertical components of the initial velocity.

v_x= __________

v_y= __________

b. Fill in the blanks in the table at the right, thus showing how the horizontal and vertical velocity changes with time.

c. At what time is Li Ping Phar at the peak of her trajectory? Explain.

5. The diagram below depict the trajectory of a projectile; the position of the projectile after each consecutive second is shown. The arrows depict the horizontal and vertical components of the velocity. Use your understanding of projectiles to fill in the blanks in the diagram.

Quiz #4

For Questions #1-5: A ball is projected into the air at an angle to the horizontal. The ball subsequently undergoes projectile motion, rising towards its peak and subsequently landing at the same vertical position a horizontal distance of 20-m away. Use this scenario to answer the following questions.

1. Which of the following describe the horizontal velocity of a projectile? List all that apply.

a. constant magnitude

b. changes by 10 m/s every second

c. initially directed in one direction and later in the opposite direction

d. is 0 m/s throughout the entir trajectory

e. is 0 m/s at the peak of the trajectory

2. Which of the following describe the vertical velocity of a projectile? List all that apply.

a. constant magnitude

b. changes by 10 m/s every second

c. initially directed in one direction and later in the opposite direction

d. the same at the beginning as at the end

e. is 0 m/s at the peak of the trajectory

3. Which of the following describe the horizontal acceleration of a projectile? List all that apply.

a. 0 m/s/s

b. changing magnitude

c. has a magnitude of 10 m/s/s

d. initially directed in one direction and later in the opposite direction

e. none of the above are true

4. Which of the following describe the vertical acceleration of a projectile? List all that apply.

a. has a magnitude of 10 m/s/s

b. changing magnitude

c. is always directed in the direction which the object moves

d.initially directed in one direction and later in the opposite direction

e. 0 m/s/s

5. At the instant when a projectile reaches the peak of is trajectory, ____.

a. there are no forces acting upon the projectile

b. the acceleration of the projectile is 0 m/s/s

c. the vertical velocity is 0 m/s

d. the horizontal velocity is 0 m/s.

e. ...nonsense! None of these are true.

For Questions #6-9: A 2.0-kg projectile is launched at an angle to the horizontal. Initially, its horizontal velocity is 30 m/s and its vertical velocity is 20 m/s. Use this information to answer the following questions.

6. The projectile will be in the air for a time of approximately ____ seconds.

a. 1.5	b. 2.0	c. 3.0	d. 3.3
e. 4.0	f. 5.0	g. 6.0	h. 10.0

7. At the peak of its trajectory, the net force acting upon the projectile is _____ N.

a. 0 N	b. 10 N	c. 20 N	d. 30 N
e. 40 N	f. 50 N	g. 60 N	h. 100 N

8. The projectile will experience a horizontal displacement of _____ m.

a. 0	b. 10	c. 20	d. 20
e. 40	f. 50	g. 60	h. 90	i. 100

9. In the moments after its initial projection, the projectile has ______. Include all that apply.

a. a greater horizontal velocity than its vertical velocity

b. a greater horizontal acceleration than its vertical acceleration

c. a greater horizontal net force than its vertical net force

d. an upward velocity and a downward acceleration

e. an upward velocity and an upward acceleration

10. On the diagrams below, draw arrows to represent the forces which act upon the football before it reaches the peak, at the peak, and after it reaches the peak. Assume the football is a "projectile" that is moving through the air from left to right. Label the force(s) according to type.

11. A golf ball leaves the club with an initial velocity of 68.2 m/s at an angle of 22.4 degrees. Determine the horizontal and vertical velocity components (i.e., v_ix and v_iy).

Demonstrate your understanding of projectiles by filling in the following table for a projectile launched at an angle to the horizontal. (Note that the initial horizontal and vertical velocities are given.)

Time (s)	v_x (m/s)	v_y (m/s)	a_x (m/s/s)	a_y (m/s/s)
0	20	30
1
2
3
4
5
6

Problem-Solving:

13. A soccer ball is kicked horizontally off a 22.0-meter high hill and lands a distance of 35.0 meters from the edge of the hill. Determine the initial horizontal velocity of the soccer ball.

14. A football is kicked with an initial velocity of 25 m/s at an angle of 45-degrees with the horizontal. Determine (a) the total time of flight, (b) the horizontal distance, and (c) the peak height of the football.

Unit 3 Quiz#3

1. Utilize a scaled vector diagram in order to determine the resultant (both the magnitude and the direction) of the following two forces. NOTE: The two forces are not at right angles.

50 N, 135 degrees

70 N, 300 degrees

On your diagram, be sure to indicate the scale, place arrowheads on all vectors, label the magnitude and direction of each vector, and clearly label the resultant.

2. Add at least two forces to each of the following three objects so that the objects will be at equilibrium. Each force which you add must either be horizontal or vertical. Clearly label their magnitude and indicate their direction by a clearly drawn arrowhead.

3. On the following diagrams, fill in all blanks and determine the acceleration (both magnitude and direction) of the object. Clearly show your calculation for the acceleration.

Diagram A

Acceleration = _________

Calculations:

Diagram B

Acceleration = _________

Calculations:

4. For Diagram B above, determine the distance which the object will be moved if the forces act upon the object for 2.0 seconds. The object is initially at rest. PSYW

5. Consider the free-body diagram on the right and the position-time and velocity-time graphs below. Which one(s) of the graphs below would be a possible representation of the motion of the object depicted in the free-body diagram? Circle any correct graphs. For the incorrect graphs, clearly explain what is incorrect using complete sentences.

Unit 3 Quiz#3

Equations:

1. If an object is at equilibrium, then the object must

a. be at rest

b. be moving at constant speed

c. be moving in the same direction

d. have an acceleration of 0 m/s2.

e. none of the above

2. If an object is at equilibrium, then all the individual forces which act upon it must be equal.

TRUE or FALSE

3. A 10-kg rock is moving through space (far from the influence of gravitational forces) at a constant speed of 1000 m/s. The amount of force required for it to maintain this state of motion is

a. 0 N

b. 100 N

c. 1000 N

d. 10000 N

e. none of the above

4.Two strings are used to suspend a 2-kg object. The object is at equilibrium (see diagram at right). The resultant of all three forces would be closest to

a. O N

b. 10 N

c. 20 N

d. 28 N

e. 48 N

5. On the following diagram, fill in all blanks and determine the acceleration (both magnitude and direction) of the object. Clearly show your calculation for the acceleration.

6. For the above diagram, determine the distance which the object will be moved if these forces act upon the object for 2.0 seconds. The object is initially at rest. PSYW

7. Add at least two forces to each of the following three objects so that the objects will be at equilibrium. Each force which you add must either be horizontal or vertical. Clearly label their manitude and indicate their direction by a clearly drawn arrowhead.

8. A 10-kg object is pulled across a rough surface at a constant velocity of 0.5 m/s. Utilize Newton's second law and an understanding of vector resolution in order to fill in the blanks in the diagram below.

9. Troy Ginometri, owner of the local floral shop, displays the sale of the month in the front window of his shop. The 20-kg flower pot is suspended by three ropes from the ceiling. The ropes make an angle of 30° with the vertical. Utilize a sketch and a trigonometric function to determine the tension in one of the ropes. PSYW

Unit 3, Quiz #3

Equations:

1. Three pictures of equal weight (20 N) are hung by wires in three different orientations. In which orientation are the wires least likely to break? Circle the correct answer.

2. A pair of forces of magnitude 5 N and 4 N are added together with a variety of directions. The maximum possible resultant which could be obtained is

a. 0 N

b. 1 N

c. 5 N

d. 9 N

e. 20 N

3. A pair of forces of magnitude 5 N and 4 N are added together with a variety of directions. The minimum possible resultant which could be obtained is

a. 0 N

b. 1 N

c. 5 N

d. 9 N

e. 20 N

4. A boat is rowed at 8 km/hr, east in a river which flows at 6 km/hr, north. The resultant speed of the boat is

a. 2 km/hr

b. 6 km/hr

c. 8 km/hr

d. 10 km/hr

e. 14 km/hr

5. A 50-N force is applied at an angle of 30 degrees north of east. This would be the same as applying two forces at

a. 43 N, east and 7 N, north

b. 35 N, east and 15 N, north

c. 25 N, east and 25 N, north

d. 43 N, east and 25 N, north

6. If an object is at equilibrium then it must

a. be at rest.

b. be moving with a constant speed.

c. not be accelerating

d. none of these

7. A northeast and a southeast vector are being added using the parallelogram method. Which diagram below illustrates the correct method of adding two such vectors.

8. What is the resultant velocity of a 5-ton airplane that normally flies at 200 km/hr if it experiences a 50-km/hr tailwind? Explain your answer.

9. When hanging clothes on a clothesline, is it best to arrange the clotheline so that it is entirely horizontal or so that it has some sag in it? Clearly explain your answer using your understanding of vector components.

10. A 1000-N force is applied at 30° east of south to a 200-kg railroad car. Use trigonometric functions to determine the eastward and southward components of this force. Please show your work below.

Show your work:

The southward component of force on the above railroad car is balanced by the northward normal force of the track pushing against the wheels of the railroad car. There is a frictional force of 400 N directed westward. Determine the acceleration of the 200-kg railroad car. PSYW

11. After its most recent delivery, the infamous stork announces the good news. If the sign has a mass of 10 kg, then what is the tensional force in each cable? Use trigonometric functions and a sketch to determine the answer. Clearly show and label all your work.

Unit 3, Quiz #3

1. Three pictures of equal weight (20 N) are hung by wires in three different orientations. In which orientation is the tension in the wires the least? Circle the correct answer and explain your reasoning using complete sentences.

2. Forces of 5 N and 12 N act at right angles on a point. The magnitude of their resultant in N is

a. 7

b. 11

c. 13

d. 17

e. 60

3. The resultant of a number of concurrent forces which are in equilibrium

a. depends on the angles between them

b. depends on the number of forces

c. depends on magnitudes and angles

d. depends on all three (a,b, & c)

e. is zero

4. Which one(s) of the following force diagrams depict an object moving to the right with constant speed? Write all possible answers (if any) in the blank: ________________

Explain your answer(s) to this question.

5. A force of 50 N acts upon an object at an angle of 30 degrees above the horizontal. This single force would be equivalent to two forces with magnitudes and directions of approximately

a. 25 N, right and 25 N, up

b. 43 N, right and 7 N, up

c. 43 N, left and 7 N, down

d. 43 N, right and 25 N, up

e. more than one of the above answers would be possible

6. If an object is at equilibrium, then all the individual forces which act upon it must be equal.

TRUE or FALSE

7. Use your understanding of force relationships and vector components to fill in the blanks in the following diagram and to determine the net force and acceleration of the object.

Fnet = ________________

a = __________________

8. Troy Ginometri, the 28-year old owner of the local floral shop, displays the sale of the month in the front window of his 2-story shop. The 4.0-kg flower pot (having a cricumference of 50-cm) is suspended by three ropes from the ceiling. The ropes make an angle of 30-degree with the vertical (i.e., a 60-degree angle with the horizontal). Determine the tension in one of the ropes. Begin with a clearly drawn sketch of a triangle depicting known information and proceed with the use of a trigonometric function and algebra to determine your answer. Partial credit is given only for work which is clearly organized and sensible. PSAYW

9. A 0.50 kg soccer ball is kicked from the top of a 14.0-meter cliff with a horizontal speed of 28.0 m/s. What distance from the bottom of the cliff does the ball land? Please show your work in an organized fashion (listing known and unknown values) to receive partial and full credit.

Unit 3 Quiz #4

1. Three pictures of equal weight (20 N) are hung by wires in three different orientations. In which orientation is the tension in the wires the least? Circle the correct answer.

2. Forces of 5 N and 12 N act at right angles on a point. The magnitude of their resultant in N is

a. 7

b. 11

c. 13

d. 17

e. 60

3. The resultant of a number of concurrent forces which are in equilibrium

a. depends on the angles between them

b. depends on the number of forces

c. depends on magnitudes and angles

d. depends on all three (a,b, & c)

e. is zero

4. A horizontal force of 100 N is needed to pull a sled forward. If the rope pulling the sled makes an angle of 30-degrees with the horizontal, the tension in the rope (in N) must be approximately

a. 50

b. 87

c. 115

d. 200

5. A 1.40-kg "Eat at Ed's" sign is hung symmetrically between two strings. The angle between the strings is 100°. Draw a clear and meaningful triangle and use trigonometric functions to predict the tension in a single string. PSYW

6. A 50-kg crate is placed on a 45° inclined plane. The coefficient of friction between the crate and the plane is 0.20. Fill in the blanks in the diagram and determine the acceleration of the crate down the plane. Clearly show your work for the acceleration calculation.

7. A 10-kg object is pulled across a rough surface. The velocity-time graph for its motion is shown at the right. Utilize Newton's second law and an understanding of vector resolution in order to fill in the blanks in the diagram below.

8. Jack and Jill climbed up a hill which had a 30° incline. They boarded a sled, with physics in head, and tried to find their accelerashine. Assuming that the surface is frictionless and that the combined mass of Jack, Jill, and the sled is 180 kg, determine their acceleration. Utilize a free-body diagram if necessary. PSAYW

Demonstrate your understanding of acceleration by filling in the velocity-time table for the motion of Jack and Jill down the hill.