school

Science Department

Physics

SPH 4A0

Name: _________________

Force,Free Body Diagrams and Hooke's Law Assignment

(1) A woman who is standing on the surface of the earth, 6.38 x 10⁶ m from its centre, has a mass of 50 kg. If the mass of the earth is 5.98 x 10²⁴ kg, what is the force of gravity on the woman?

(2) The force of gravity on a spacecraft some distance from the earth is 1200 N. What would that force be if its distance to the Earths centre were one-third as great?

(3) A boy pushes horizontally on a 15 kg wagon and it accelerates at 1.5 m/s². If frictional forces total 65 N, what force must he be exerting?

(4) A pull toy consists of 2 carts joined together by a short string and a longer string, for pulling, attached to the front cart. If a child pulls the toy with a horizontal force of 6.0 N, what force must the short string be able to withstand?

5) A boy on a bicycle drags a wagon full of newspapers using a force of 50 N. If the mass of the wagon and papers is 25kg, what is the coefficient of friction between the wagon and the ground?

(6) With what force will the boy have to pull the wagon when half the papers are gone. The mass of just the papers is 12kg?

(7) A 1000 kg car accelerates at 2.0m/s² to the right. The cars engine supplies a force of 3500N to the right. What is the force of friction and coefficient of friction between the tires and the pavement?

Kinematics Problems

1. Viking I, the first space craft to reach and land on Mars, travelled 7.00x10⁸ m in 303 days. What was its average speed in km/s?

2. The speed limit on highways and expressways is 100km/h. If you see something in the road ahead of you it usually takes about 1.0s to fully apply the brakes. How far will the car travel in that time?

3. A light plane leaves Albany and travels due south 80 km towards Kingston, New York. After arriving over Kingston, the pilot is informed that the navigational equipment at the airport is malfunctioning. He is advised to land at an airport near Hudson, New York, located 18 km to the north of Kingston. The trip from Albany to Kingston takes 20 minutes, and the trip from Kingston back to the airport in Hudson takes 8.0 minutes.

a) What is the total distance travelled?

b) What is the total displacement ?

c) What is the average velocity ( vector quantity) for the plane in traveling from:

i) Albany to Kingston?

ii) Kingston to Hudson?

iii) Albany to Hudson?

d) What is the average speed for the entire trip?

4. Austin is about 50 km from San Marcos. A freight train starts out from San Marcos for Austin at 50 km/h. At the same time a passenger train leaves Austin for San Marcos at 75 km/h. How much time passes before they meet one another in minutes?

Projectile Motion Problems

1. A long jumper leaves the ground at an angle of 20⁰ to the horizontal and at a speed of 11m/s.. How far does he jump? What is the maximum height reached by the jumper?

2. Harry gives Sam a 30m head start in the 100m dash. Harry can run at 10 m/s, while Sam only runs at 6.0m/s. Draw a position-time graph for a 100m dash, plotting both runners.

a) Does Harry win? If so at what time and place does he catch up to Sam

b) How much of a head start would Sam require to win the race?

3. A motorboat is headed [E30⁰N] with its engine set to move the boat at 30km/h in still water. There is a current of 15 km/h [S]. What is the velocity of the boat relative to the shore?

4. A pilot in training is given the following path to follow. Fly at 400 km [W35⁰S] , followed by 250km [N57⁰E] followed by 100km [E45⁰S] followed by 145km [S18⁰W]. Determine the position of the aircraft.

4. An astronaut on the moon throws a wrench straight up at 4.0m/s. Three seconds later it has a velocity of 0.8m/s[down].

a) What was the acceleration of the wrench after it left the astronauts hand?

b) How high above the point of release was the wrench at 3.0s?

c) How long did it take the wrench to return to its point of release?

d)What was the maximum height reached by the wrench?

6.A baseball is hit in such a way that it just clears a wall that is 3 m tall 130 m from the plate. The ball leaves the bat at an angle of 35^oto the horizontal and 1m above the ground. Find its initial velocity.

Science Department Name:__________________

Physics SPH4A0

Chapters 1 and 2: Test A Mark:_____/65

PART A: Multiple choice. For each of the following questions, select

the correct response. Place the letter in the space provided

to the right. (32 Marks)

1. Displacement:

a. describes magnitude and direction of change in position

b. includes the total length of the path travelled _____

c. is a scalar quantity

d. is always the same as the displacement

e. all of the above

REFER TO FIGURE 1 FOR QUESTIONS # 2 - 4.

FIGURE 1: A person starts at position 1, travels to position 2,

then to three, and stops at position 4.

2. What is the total distance travelled?

a. 20 km [E] b. 95 km _____

c. 120 km d. 70 km

3. What is the displacement?

a. -5 km [W] b. -5km [E] _____

c. 95 km [W] d. 5 km [E]

4. If the trip took 9 hours, find the average speed.

a. 10.1 km/h b. 3.3 km/h [W] _____

c. 13.3 km/h d. 7.8 km/h

5. Uniform motion occurs when:

a. the speed is constant and the direction changes

b. the velocity is constant and the direction changes _____

c. the speed changes and the direction is constant

d. the speed is constant and the direction is the same

6. Acceleration is equal to:

a. the slope of a acceleration - time graph

b. the slope of a speed - time graph _____

c. the slope of an velocity - time graph

d. the area under the displacement - time graph

7. A car travels with a velocity of 180 km/h [W]. What is its

displacement if it travels at this velocity for 3.5 h?

a. 63 000 m [W]

b. 630 km [W] _____

c. 51 m [W]

d. 0.02 m [W]

8. Which of the following are vectors:

i) distance ii) displacement iii) acceleration

iv) velocity v) speed vi) time

a. i, ii

b. ii, iii, iv _____

c. i, iv

d. ii, iv, v

e. all

9. Using the graph shown which one of the following

statements is true?

a. V_c > V_a > V_b

b. V_b > V_a > V_c _____

c. V_a > V_b > V_c

d. V_a > V_c > V_b

10. When will the displacement and distance and therefore speed

and velocity be the same in magnitude?:

a. always

b. never

c. when motion is in one direction _____

d. when motion is in different directions

11. The displacement in any interval is given by the area under the:

a. speed - time graph

b. distance - time graph _____

c. velocity - time graph

d. acceleration - time graph

12. A horizontal line on a displacement - time graph suggests:

a. the object is stopped

b. the object is moving at a constant velocity _____

c. the object is accelerating

d. the object is moving extremely fast

13. A horizontal line on a velocity - time graph suggests:

a. the object is stopped

b. the object is moving at a constant velocity _____

c. the object is accelerating

d. the object is moving extremely fast

REFER TO FIGURE 2 FOR QUESTIONS # 14 - 21

FIGURE 2: Position - time graph for truck driver trying to find

a certain house on a long straight street.

14. The truck is stopped in section:

a. C b. D c. A d. B e. None of these _____

15. The truck is northbound in sections:

a. A,B,D b. B _____

c. A,D d. C e. A,C,D

16. The objects position is at 100 m at:

a. 7min b. never c. 30 s d. 11min _____

17. The object is at 15 m [N] at:

a. 3-5 min only b. never c. 3-5 and 6.8 mind. 30 - 40s _____

18. The velocity in section B is:

a. 15 m/s [N] b. 0 m/s [N] _____

c. -5.0 m/s [N] d. 20 m/s [N]

19. The speed in section A is:

a. 15 m/min [N] b. 0 m/min c. 10 m/min d.15.0 m/min _____

20. The total distance travelled is:

a. 60 m b. 0 m c. 60m [N] d. 50 m [N] _____

21. The displacement for the entire trip is:

a. 60 m b. 0 m c. 60m [N] d. 50 m [N] _____

REFER TO FIGURE 3 (v - t graph) FOR QUESTIONS # 22 - 27

FIGURE 3: Velocity - Time graph for a trip taken on a bicycle

22. The bicycle is moving south at a constant speed in section:

a. G b. I _____

c. E d. H

23. The displacement in section B is:

a. 16 m [N] b. 4 m [N] _____

c. 5 m [S] d. 16 m [S]

24. The bicycle is moving south in sections:

a. G to I b. A to E _____

c. A, C and I d. B,E,F

25. The bicycle is decelerating in sections:

a. E, G and I b. B, D, F and H _____

c. A, D d. E, I

26. The average acceleration for the time interval t = 52 s

to t = 56 s is:

a. 2.0 m/s² [N] b. 0 m/s² _____

c. 0.83 m/s² [N] d. -1.4 m/s² [S]

27. The instantaneous acceleration at time t = 1.5 s is:

a. 0 m/s² b. 0.5 m/s² [N] _____

c. 4 m/s² [N] d. 1.3 m/s² [N]

28. If the speed of light is 3.00 x 10⁸ m/s, what is the speed

in units of km/h?

a. 1.08 x 10⁹ km/h

b. 83.3 km/h _____

c. 8.33 x 10⁷ km/h

d. 1.80 x 10¹³ km/h

29. A car accelerates at a constant rate from 5 m/s [E] to

30 m/s [E] in 3 seconds. What is the acceleration?

a. 0.12 m/s² [E] b. 0.83 m/s² [E] _____

c. 8.3 m/s² [E] d. 75 m/s² [E]

30. A driver entering the outskirts of a city takes her foot off

the accelerator so that her car slows down from 110 km/h [E]

to 60 km/h [E] in 15 s. Find the car's average acceleration:

a. -3.3 km/h² [E]

b. -3.3 (km/h)/s [E] _____

c. 0.3 (km/h)/s [E]

d. 0.3 km/h² [E]

31. How long will it take a car travelling with an average

acceleration of 120 (km/h)/s [W] to change its velocity from

50 km/h [W] to 90 km/h [W]?

a. 3 s b. 0.3 h _____

c. 0.3 s d. 4800 s

32. Which graph describes an object moving with uniform acceleration?

_____

a. b. c. d.

PART B: Uniform vs Non Uniform Motion (3 Marks)

1. Complete the following chart. State the type of motion that

describes each situation (ie. Uniform or Non-Uniform).

Description	Type of Motion
a satellite orbits the earth at constant speed
a car travels along a straight section of an expressway at a constant speed
a steel ball is dropped from your raised hand to the floor

PART C: Manipulating Equations.

1. What is Jake's displacement in 42 s if he travels with uniform motion

at a velocity of 8.6 m/s [S]. Express answer in scientific notation

with the correct number of significant digits. (5 Marks)

2. During the Summer Olympics a sprinter running at 12.6 m/s [W]

crosses the finish line and comes to rest in 3.8 s. What is the

sprinter's average acceleration? Express your answer in scientific notation with the correct number of significant digits. (5 Marks)

PART D Graphs (20 Marks)

1. Below is a d - t graph for a Remote Control Dune Buggy. Using the

graph, Find the following:

a) distance, average speed, displacement, average velocity for the

time interval t = 16s to t = 30s (5 Marks)

b) instantaneous velocity at: i) t = 13s (2 Marks)

ii) t = 9s (2 Marks)

c) total displacement for the interval t = 0 to t = 34s. (1 Mark)

**NOTE**: Show all slopes on graph. Express all non-zero answers in scientific notation with 2 significant digits. Show the numbers

you are using to get your answers.

2. For the following velocity - time graph perform the following:

a. Calculate the acceleration in sections A, C, and E. (3 Marks)

b. Calculate the displacement in each section. (6 Marks)

c. Calculate the total displacement for the entire interval. (1 Mark)

NOTE: Express all non zero answers in scientific notation with 2 significant digits. Show all the numbers you are using to get your answers.

Science Department

Physics

SPH 4A0

Name: _______________

Vectors Take Home Test

1) Connie has her eye on a new dress for the prom and is trying to find her way to the mall to buy it. She starts at her home and walks 600m [E47^oN], then 500m [N38^oW], then 300m [W29^oS], and finally 400m [S13^oE]. Using components of vectors, find Connie's resultant displacement.

2) Martha and Christine are in a canoe paddling "north" across a river at 3.0 m/s. (The canoe is always kept pointed at right angles to the river.) The river is flowing east at 4.0 m/s and is 100 m wide.

(a) What is the velocity of the canoe relative to the river bank?

(b) Find the time required to cross the river.

3) Mindy has recently earned her pilot's licence and wishes to take her classmates for a ride in her brand new DC-9. (She always gets what she wants.) After reaching the proper altitude, Mindy says that she now wants to fly "east". The plane has a velocity of 350 km/h relative to the air. A wind is blowing at 65 km/h [N]. Find the proper heading and the magnitude of the plane's velocity relative to the ground.

4. A boy in a car travelling at 10km/h [N] wants to throw a ball to a girl standing on the right hand side of the road. He is able to throw the ball at 20km/h. He wants the ball to go straight east, directly to her.

a) Relative to the car, which way should he throw the ball in order to do this?

b) Relative to the ground how fast will the ball travel to reach her?

5. A ball rolls up a hill, starting at 10m/s [up], and accelerating at 3.0m/s² [down]. What is its velocity after

a) 1.0s?

b) 3.0s?

c)4.0s?

6. A ship travels at 30km/h [N30^oE] for 10h, and then at 20km/h [W60^oS] for 17h. What is its total displacement?

7. A man is standing on the deck of a freighter heading north, at 10km/h. He measures the wind velocity to be 10km/h [E]. What is the actual wind velocity?

8. A pilot wants to fly a huge square path over the ground, 100 km[N], 100km[E], 100km[S] and 100km [W]. Her plane has an air speed of 100km/h. There is a 50 km/h wind blowing to the south. For each leg of the trip determine:

a) the ground speed

b) the heading

c) the time in minutes.

d) What would be the savings in time if there were no wind?

school

Science Department

Physics

SPH 4A0

Name: _________________

Force, Work and Energy Assignment

(1) A woman who is standing on the surface of the earth, 6.38 x 10⁶ m from its centre, has a mass of 50 kg. If the mass of the earth is 5.98 x 10²⁴ kg, what is the force of gravity on the woman?

(NOTE: There are two methods to arrive at a solution for this problem. Calculate the answer using BOTH methods.)

(2) The force of gravity on a spacecraft some distance from the earth is 1200 N. What would that force be if its distance to the Earths centre were one-third as great?

(3) A boy pushes horizontally on a 15 kg wagon and it accelerates at 1.5 m/s². If frictional forces total 65 N, what force must he be exerting?

(5) A boy on a bicycle drags a wagon full of newspapers at 1.2 m/s for 45 minutes using a force of 50 N. How much work has the boy done?

(6) How much power does the boy in question (5) generate?

(7) A 1000 kg car moves from point A to point B and then to point C. What is its potential energy at:

(a) point B relative to point A?

(b) point C relative to point A?

(8) A roller coaster is shown in the following figure. Assuming no friction, calculate the speed at points B and C assuming it has a speed of 2.0 m/s at point A.

Name:__________________________

School

Science Department

Physics

SPH 4A1

KINEMATICS TEST

PART A - Motion with Uniform Acceleration (16 marks)

Marks

4 (1) A car travelling at 25 m/s accelerates at 5.0 m/s² for 12 s. What is its displacement during this interval?

6 (2) An airplane taking off from an airfield has a run of 370 m. If it starts from rest, moves with constant acceleration, and makes the run in 30 s, with what velocity does it take off?

6 (3) A bullet that is shot vertically into the air has an initial velocity of 500 m/s.

(a) How long does it take before the bullet stops rising?

(b) How high does the bullet go?

PART B - Forces (9 marks)

5 (4) A woman who is standing on the surface of the earth, 6.38 x 10⁶ m from its centre, has a mass of 50 kg. If the mass of the earth is 5.98 x 10²⁴ kg, what is the force of gravity on the woman?

(NOTE: There are two methods to arrive at a solution for this problem. Calculate the answer using BOTH methods.)

4 (5) The force of gravity on a spacecraft some distance from the earth is 1200 N. What would that force be if its distance to the Earths centre were one-third as great?

PART C - Newton's Laws of Motion (10 marks)

5 (6) A boy pushes horizontally on a 15 kg wagon and it accelerates at 1.5 m/s². If frictional forces total 65 N, what force must he be exerting?

5 (7) A pull toy consists of 2 carts joined together by a short string and a longer string, for pulling, attached to the front cart. If a child pulls the toy with a horizontal force of 6.0 N, what force must the short string be able to withstand?

PART D - Work, Power, and Energy (22 marks)

5 (8) A boy on a bicycle drags a wagon full of newspapers at 1.2 m/s for 45 minutes using a force of 50 N. How much work has the boy done?

2 (9) How much power does the boy in question (9) generate?

5 (10) A 1000 kg car moves from point A to point B and then to point C. What is its potential energy at:

(a) point B relative to point A?

(b) point C relative to point A?

10 (11) A roller coaster is shown in the following figure. Assuming no friction, calculate the speed at points B and C assuming it has a speed of 2.0 m/s at point A.

school

Science Department

Physics

SPH 4A0

Name:_________________

KINEMATICS TEST

PART A - Short Answer(6 marks)

2 1) Sketch a velocity-time graph for an object that falls from rest. Assume that it accelerates uniformly at the beginning and then gradually decreases its acceleration until it falls with uniform velocity (similar to a skydiver's fall before the parachute opens).

2 2) Melisa throws a ball straight up in the air. What is its acceleration at the instant it reaches its highest point? Explain.

2 3) Explain why the value for g (9.8m/s²) is usually over-estimated when performing free fall experiments

(2 reasons).

PART B - Motion with Uniform Acceleration (20 marks)

4 1) A car travelling at 25 m/s accelerates at 5.0 m/s² for 12 s. What is its displacement during this interval?

6 2) An airplane, taking off from an airfield, has a run of 370 m. If it starts from rest, moves with constant acceleration, and makes the run in 30 s, with what velocity does it take off?

10 3) A subway train starts from rest at a station and accelerates at a rate of 2.0 m/s² for 10 s. It then runs at constant speed for 30 s and slows down at -4.0 m/s² until it stops at the next station. Find the TOTAL distance covered.

PART C - Free-Falling Bodies (20 marks)

7 1) A bullet that is shot vertically into the air has an initial velocity of 500 m/s.

(a) How long does it take before the bullet stops rising?

(b) How high does the bullet go?

7 2) Sarah is in a hot air balloon that is rising vertically with a velocity of 5.0 m/s. She releases a sandbag at an instant when the balloon is 20 m above the ground.

(a) Find the position and velocity of the sandbag 2 s after its release.

6 3) Nicole throws a stone straight down from the top of a cliff with an initial velocity of 6.0 m/s. It reaches the bottom in 3 s. How high is the cliff?

school

Science Department

Physics

SPH 4A0

Name:_________________

KINEMATICS TEST

PART A - Short Answer(6 marks)

2 2) Melisa throws a ball straight up in the air. What is its acceleration at the instant it reaches its highest point? Explain.

2 3) Explain why the value for g (9.8m/s²) is usually over-estimated when performing free fall experiments

(2 reasons).

PART B - Motion with Uniform Acceleration (20 marks)

4 1) A car travelling at 25 m/s accelerates at 5.0 m/s² for 12 s. What is its displacement during this interval?

6 2) An airplane, taking off from an airfield, has a run of 370 m. If it starts from rest, moves with constant acceleration, and makes the run in 30 s, with what velocity does it take off?

PART C - Free-Falling Bodies (20 marks)

7 1) A bullet that is shot vertically into the air has an initial velocity of 500 m/s.

(a) How long does it take before the bullet stops rising?

(b) How high does the bullet go?

7 2) Sarah is in a hot air balloon that is rising vertically with a velocity of 5.0 m/s. She releases a sandbag at an instant when the balloon is 20 m above the ground.

(a) Find the position and velocity of the sandbag 2 s after its release.

6 3) Nicole throws a stone straight down from the top of a cliff with an initial velocity of 6.0 m/s. It reaches the bottom in 3 s. How high is the cliff?