Excursions in Physics

First Hour Exam

June 15, 1998

Statistics:

High score: 98%

Mean: 71%

Low: 45%

Enter all your answers in the "scantron sheet" or the "bubble sheet". Turn in only that sheet. Anything you write on this exam will not be seen or used or considered or graded. Be sure your name is on the "bubble sheet" you hand in. Be sure your name is bubbled-in. Be sure your answers are recorded correctly.

For every question, also consider the following as a possible answer:

e) none of the above

Possibly useful information:

v = x / t

a = v / t

v = v_i + a t

x = x_i + v _i t + (¹/₂) a t²

v = r

F = ma

F₁₂ = - F₂₁

w = mg

g = 9.8 m/s² = 10 m/s²

For every question, also consider the following as a possible answer:

e) none of the above

 

1. Kinematics is a description of motion. Motion was first well understood

a) by Aristotle and the ancient Greeks

b) by Ptolemy in Egypt

c) by Galileo in Italy

d) not until the beginning of the twentieth century

 

2. To measure the time needed to investigate motion,

a) Aristotle used the pendulum clock which had just been invented

b) Ptolemy used a sundial

c) Galileo invented his own water clocks

d) Newton invented the pendulum clock

 

3. Velocity is the time rate of change of

a) acceleration

b) speed

c) displacement

d) momentum

 

4. Acceleration is the time rate of change of

a) velocity

b) displacement

c) distance

d) momentum

 

5. Acceleration might be described as telling

a) where an object is located relative to an origin or reference point.

b) how fast something is moving.

c) how fast something is getting faster.

d) how long an object has been moving.

 

6. What is the average speed of a motorcycle that travels 30 m in 3 s?

a) 90 m/s

b) 30 m/s

c) 10 m/s

v_avg = x / t = 30 m / 3 s = 10 m/s

d) 6 m/s

 

7. What is the average speed of a car that travels 75 km in 3 h?

a) 225 km/h

b) 25 km/h

v_avg = x / t = 75 km / 3 h = 25 km/h

c) 15 km/h

d) 9.8 km/h

 

8. Consider a car that starts at rest and accelerates at 2 m/s² for 3 seconds. At that time, t = 3 s, how fast is it going?

a) 30 m/s

b) 19 m/s

c) 16 m/s

d) 6 m/s

v = v_i + a t

v = 0 + (2 m/s²) (3 s)

v = 6 m/s

 

9. Consider a train that has an acceleration of 2 m/s². Initially, at time t = 0, it has a velocity of v_i = 10 m/s. What is its velocity at t = 4 s?

a) 26 m/s

b) 19 m/s

c) 16 m/s

d) 6 m/s

e) none of the above

v = v_i + a t

v = 10 m/s + (2 m/s²) (4 s)

v = (10 + 8) m/s

v = 18 m/s

 

10. Consider a train that starts at rest and accelerates at 2 m/s² for 4 seconds. At that time, t = 4 s, how far has it gone?

a) 32 m

b) 16 m

x = x_i + v _i t + (¹/₂) a t²

x = 0 + 0 + (¹/₂) (2 m/s²) (4 s)²

x = 0 + 0 + (¹/₂) (2 m/s²) (16 s²)

x = 16 m

c) 12 m

d) 8 m

 

11. Consider a ball that is thrown upward at the edge of a canyon with an initial velocity of 20 m/s. Three seconds later, what is its velocity?

a) 30 m/s

b) 15 m/s

c) - 10 m/s

v = v_i + a t

v = 20 m/s + (- 10 m/s²) (3 s)

v = (20 - 30) m/s

v = -10 m/s

d) - 20 m/s

 

12. Consider a ball that is thrown straight upward at the edge of a canyon with an initial velocity of 20 m/s. Three seconds later, where is it located? Take its initial position, at the edge of the canyon, to be the origin; that is, y_i = 0.

a) 30 m

b) 15 m

x = x_i + v _i t + (¹/₂) a t²

y = y_i + v _i t + (¹/₂) a t²

y = 0 + (20 m/s) (3 s) + (¹/₂) ( - 10 m/s²) (3 s)²

y = 0 + 60 m + (¹/₂) ( - 10 m/s²) (9 s²)

y = 0 + 60 m - 45 m

y = (60 - 45) m

x = 15 m

c) - 10 m

d) - 30 m

 

13. Consider a ball that is thrown horizontally from the edge of a building with an initial velocity of 25 m/s. The edge of the building is 5 m above the driveway below. How far from the building does the ball strike the driveway?

a) 5 m

b) 10 m

c) 20 m

d) 25 m

First, we must find out how long the ball is in the air.

v_yi = 0

y_i = 0

How long does it take the ball to reach y = - 5 m (the y-position of the driveway)?

y = y_i + v _i t + (¹/₂) a t²

y = 0 + 0 + (¹/₂) ( - 10 m/s²) t²

y = (¹/₂) ( - 10 m/s²) t² = - 5 m

- 5 t² = - 5

t² = 1

t = 1 s

Now, how far does it travel horizontally in this time of one second?

x = x_i + v _i t + (¹/₂) a t²

The horizontal acceleration is zero; the horizontal motion is motion at constant velocity.

x = x_i + v _i t

x = 0 + (25 m/s) (1 s)

x = 25 m

 

14. When a ball or stone or other object is thrown or hit or fired, and air resistance can be neglected, the resulting motion is known as projectile motion The path of an object in projectile motion is

a) a straight line

b) a hyperbola

c) a parabola

d) a quadrant of a circle

 

15. Projectile motion is a combination of

a) horizontal motion with constant, non-zero acceleration and vertical motion with constant velocity

b) horizontal motion with constant non-zero acceleration and vertical motion with constant, non-zero acceleration

c) horizontal motion with constant velocity and vertical motion with constant, non-zero acceleration

d) horizontal motion with constant velocity and vertical motion with constant velocity

 

16. Consider a ball thrown from a level surface with an initial upward velocity of 10 m/s and an initial horizontal velocity of 5 m/s. How long is the ball in the air?

a) 1.0 s

b) 1.5 s

c) 2.0 s

d) 4.0 s

 

17. Consider a ball thrown from a level surface with an initial upward velocity of 10 m/s and an initial horizontal velocity of 5 m/s. Where does it land? That is, measured from its initial position, where does it come back to and strike the level surface?

a) 5 m

b) 10 m

In the previous problem, we already found that the ball is in the air for

t = 2 s

It moves horizontally at constant speed

x = v t

x = (5 m/s) (2 s)

x = 10 m

c) 15 m

d) 20 m

 

18. Newton's First Law of Motion states that, in the absence of a net force, an object in motion will

a) continue along the same straight line with a decrease in speed

b) continue in motion with the same speed along the same straight line

c) continue in motion but slow down until it stops

d) eventually come to rest

 

19. Mass is a measure of

a) the volume of an object

b) the velocity of an object

c) how difficult it is to change the motion of an object

d) the size of an object

 

20. The weight of an object is

a) the same thing as the mass of an object

b) the sum of all the forces on an object

c) the force of gravity on an object

d) always less than the mass, except in a vacuum

 

21. The net force on a 1-kg object, at rest, is

a) 9.8 N

b) 4.9 N

c) 1.00 N

d) zero

For an object to remain at rest, the net force must be zero.

 

22. The net force on a 1-kg object, in free fall (neglecting air resistance), is

a) 9.8 N

In free fall, the only force on an object is its weight, the force of gravity

w = mg

w = (1 kg) (9,8 m/s²)

w = 9.8 N

b) 4.9 N

c) 1.00 N

d) zero

 

23. Harry the Painter has a weight of 500 N. When he is suspended as shown in the sketch here, what is the tension in the rope?

a) 1000 N

b) 500 N

The rope pulls UP on Harry only once. Therefore its single upward force must just balance the downward force of gravity, Harry's weight (500 N). So the force exerted by the single upward force of the rope is 500 N. This is the tension in the rope. It is the force exerted throughout the rope. (The rope also pulls on the flagpole with an identical force of 500 N).

c) 250 N

d) 25 N

 

24. Newton's Second Law of Motion explains the cause of motion and may be stated as

a) "All motion is relative."

b) "All objects fall with the same velocity."

c) "The acceleration of an object is proportional to the net force on the object and inversley proportional to the object's mass."

We could write that as

a = F / m

which is equivalent to our more familiar

F = ma

d) "The acceleration of an object is proportional to the product of the object's mass and the net force on it."

 

25. Newton's Second Law of Motion explains the cause of motion and may be stated as

a) The net force on an object is inversely proportional to its weight.

b) The net force on an object produces an acceleration that is proportional to the time of action of that force.

c) The net force on an object is equal to the product of the mass of that object and its acceleration.

And, indeed, that is just

F = m a

d) The net force on an object is inversely proportional to the mass of the object.

 

26. A force of 24 N acts on an object whose mass is 8 kg.

This causes the object to accelerate at

a) 2 m/s²

b) 3 m/s²

F = m a

24 = 8 (a)

a = 3

a = 3 m/s²

c) 4 m/s²

d) 6 m/s²

 

27. A car, with mass of 1,000 kg, accelerates at 2 m/s².

The net force exerted on the car must be

a) 500 N

b) 1,000 N

c) 2,000 N

F = m a

F = (1,000 kg) (2 m/s²)

F = 2,000 N

d) 10,000 N

 

28. The weight of a 1,000-kg car is

a) 500 N

b) 1,000 N

c) 2,000 N

d) 10,000 N

w = m g

w = (1,000 kg) (10 m/s²)

w - 10,000 N

 

29. A firefighter, whose weight is 500 N, slides down a pole with an acceleration of 2 m/s². The forces that act on her are her weight pulling her down and the force of friction pulling up on her to slow herdown. The force of friction must be

a) 100 N

b) 200 N

c) 400 N

F = m a

F_net = m a

w = m g

w = 500 N = m (10 m/s²)

m = 50 kg

F_net = m a

F_net = (50 kg) (2 m/s²) = 100 N

F_net = F_grav - F_f

(I am now taking down as positive).

F_net = F_grav - F_f = m a

F_net = 500 N - F_f = (50 kg) (2 m/s²)

500 N - F_f = (50 kg) (2 m/s²) = 100 N

500 N - F_f = 100 N

F_f = 400 N

d) 500 N

 

30. Newton's Third Law of Motion may be stated as

a) The force that object A exerts on object B is proportional to the sum of their masses and inversely proportional to the distance between their centers.

b) The force that object A exerts on object B is proportional to the sum of their masses and inversely proportional to the square of distance between their centers.

c) The force that object A exerts on object B is equal to the force that object B exerts on object A but is in the opposite direction.

d) The force that object A exerts on object B is equal to the distance between object B and object A.

 

31. Newton's Third Law of Motion may be paraphrased as

a) "You can not touch a moving object without affecting its motion."

b) "You can not touch without being touched."

c) "You can not touch a hot flame without being burned."

d) "You can touch a moving object &emdash; if you are quick and careful."

 

32. Suppose you are driving along in an open car and throw a ball straight up into the air. While the ball is still in the air you step on the accelerator and speed up. Where does the ball land relative to the car?

a) behind the car

b) back into the car

c) in front of the car

 

33. Sir Isaac Newton

a) first discovered the Law of Falling Bodies while at the University of Pisa.

b) was a close friend of Liebnitz and encouraged his early development of calculus.

c) made great advances in Mechanics, Gravity, Optics, and Mathematics.

d) used water clocks of his own invention to aid sailors in determining their longitude.

 

 

34. Galileo

a) may be called the Father of Modern Optics.

b) wrote his findings in Polish while at the University of Paduah.

c) may be called the Father of Modern Science.

d) wrote his findings about Gravity and explained calculus.

 

 

35. The hallmark of Modern Science is that

a) theories are accepted or rejected based upon the background or reputation of the scientists who propose them (horrors!)

b) predictions of theories must be tested by and agree with experimental results.

c) theories must have elegant mathematical equations.

d) predictions of theories must not contradict established authorities (such as Plato or Pythagores)

 

 

36. When applying Newton's Second Law of Motion, F = ma,

a) F is always the largest force present.

b) F is always the net force -- or the sum of all the forces present.

c) m is always the largest mass in the system.

d) m must be the smallest mass in the system.

 

 

37. When using Newton's Third Law of Motion, F₁₂ = - F₂₁, the two forces

a) always cancel so this applies only to systems in equilibrium.

b) always act on different objects.

c) must act on the same object.

d) are always perpendicular to each other.

 

 

38. What value will the spring scale read in the system shown above?

a) zero

b) 25 N

c) 50 N

d) 100 N

 

 

39. What is the net force on a 1-kg laboratory cart which accelerates at 3 m/s²?

a) 3 N

F = m a

F = (1 kg) (3 m/s²)

F = 3 N

b) 10 N

c) 30 N

d) 45 N

 

 

40. What acceleration is produced if a net force of 500 N is applied to a 1000-kg car?

a) 10 m/s²

b) 5.0 m/s ²

c) 2.0 m/s ²

d) 0.5 m/s ²

F = m a

500 N = (1,000 kg) (a)

a = (500 N) / (1,000 kg)

a = 0.5 m/s²