Excursions in Physics

First Hour Exam

17 September 1998

Statistics:

High score: 95%

Mean: 76.2%

Low: 37.5%

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 = m a

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 intervals 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 may 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 60 m in 4 s?

a) 30 m/s

b) 15 m/s

v_avg = ^{60 m}/_{4 s} = 15 ^m/_s

c) 10 m/s

d) 9.8 m/s

 

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

a) 25 km/h

v_avg = ^{75 km}/_{3 h} = 25 ^km/_h

b) 15 km/h

c) 10 km/h

d) 9.8 km/h

 

8. Consider a train that has an acceleration of 3 m/s². Initially, at time t = 0, it has a velocity of v_i = 20 m/s. What is its speed at t = 3 s?

a) 50 m/s

b) 40 m/s

c) 33 m/s

d) 29 m/s

v = v_i + a t

v = 20 ^m/_s + (3 m/s²)(3 s)

v = (20 + 9) ^m/_s

v = 29 ^m/_s

 

9. Consider a car that starts at rest [v_i = 0] and accelerates at 2 m/s² for 3 seconds.

At that time, t = 3 s, how fast is it going?

a) 18 m/s

b) 12 m/s

c) 9 m/s

d) 6 m/s

v = v_i + a t

v_i = 0

v = 0 + (2 m/s²)(3 s)

v = 6 m/s

 

10. Consider a car that starts at rest [v_i = 0] and accelerates at 2 m/s² for 3 seconds.

At that time, t = 3 s, how far has it gone?

a) 18 m

b) 9 m

x = ¹/₂ (2 m/s²) (3 s)²

x = 9 m

c) 6 m

d) 3 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

Of course, the minus sign means it is moving downward.

d) - 30 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

y = y_i + v_yi t + (¹/₂) a_y t²

y = 0+(20 m/s)(3 s)+(0.5)( - 10 m/s²)(3 s)²

y = (20 m/s)(3 s) - (0.5)(10 m/s²)(3 s)²

y = (60 - 45) m

y = 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 20 m/s. 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) 15 m

d) 20 m

How long is the ball in the air?

v_yi = 0 (its initial velocity is horizontal).

How long does it take the ball to fall 5m?

y = y_i + v_yi t + (¹/₂) a_y t²

y = 0 + 0 + (0.5)( - 10 m/s²) t²

When the ball strikes the ground,

y = - 5 m

y = - 5 m = (0.5)( - 10 m/s²) t²

- 5 m = ( - 5 m/s²) t²

t =1 s

Now that we know how long, we can (finally) ask "how far". How far does the ball travel in a time of 1 s?

x = v_xi t

x = (20 m/s) (1 s)

x = 20 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) 0.5 s

b) 1.0 s

c) 2.0 s

While there are several ways to solve this, one direct method is to find the time that gives y = 0

y = y_i + v_yi t + (¹/₂) a_y t²

y = 0 + (10 m/s) t + (0.5)( - 10 m/s²) t²

Set y = 0

0 = 10 t - 5 t²

0 = (10 - 5 t) t = 0

t = 0 is an "uninteresting" solution

10 - 5 t = 0

5 t = 10

t = 2 seconds

Another way is just to think of the velocity at the end of each second:

t = 0 s, v_y = 10 m/s

t = 1 s, v_y = 0 m/s

t = 2 s, v _y = - 10 s

At the end of two seconds, the vertical component of the velocity is just the opposite of the initial vertical component. In discussing both straight, 1-D free fall and projectile motion, we have seen that this happens when the vertical position is back to the original.

Or, we could look at the table above and see that it will take one second to reach the top of its motion. Therefore, it will require the same one second to come on back down -- for a total time in the air of t = 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 question, we found that the ball was in the air for two seconds. How far, horizontally, does it move in that time?

x = v_xo 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) eventually come to rest

b) continue in motion but slow down until it stops

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

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

 

19. 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 inversly proportional to the object's mass."

a = F/m

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

 

20. 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.

F = m a

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

 

21. Mass is a measure of

a) the volume of an object

b) the size of an object

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

d) the velocity of an object

 

22. 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, even in a vacuum

 

23. 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

 

24. The net force on a 1-kg object, in free fall, is

a) 9.8 N

w = m g

w = (1 kg) (9.8 m/s²)

w = 9.8 N

b) 4.9 N

c) 1.00 N

d) zero

25. 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

Harry's weight of 500 N (down) is supported by the tension in the rope (up) so the rope must exert an upward force of 500 N. That is the tension in the rope.

c) 250 N

d) 25 N

[[ The original version of the homework solution for this problem was confusing or misleading with the diagrams on the web appearing differently than the ones in the textbook. The above answer, b) 500 N, and the above explanation are correct. However, I realize that the original version of the homework solution could lead you to think the answer should have been c) 250 N. Therefore, if you did choose that incorrect answer, it has been counted as correct. Take a look at this question in the homework solution now (Ex 4.22). ]]

 

26. A force of 24 N acts on an object whose mass is 6 kg. This causes the object to accelerate at

a) 2 m/s²

b) 4 m/s²

F = m a

24 N = (6 kg) (a)

24 N = (6 kg) (4 m/s²)

a = 4 m/s²

c) 6 m/s²

d) 10 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 = mg

w = (1,000 kg) (10 m/s²)

w = 10,000 N

 

29. A fireman, whose weight is 500 N, slides down a pole with an acceleration of 3 m/s². The forces that act on him are his weight pulling him down and the force of friction pulling up on him to slow him down. The force of friction must be

a) 90 N

b) 150 N

c) 350 N

w = m g

w = 500 N means m = 50 kg

500 N = (50 kg) (10 m/s²)

Now we are ready to use Newton's Second Law,

F = ma

But, remember, that is always the net force,

F_net = F_gravity - F_friction

F_net = w - F_friction

F_net = 500 N - F_friction

F_net = m a = (50 kg) (3 m/s²) = 150 N

500 N - F_friction = 150 N

F_friction = 350 N

d) 500 N

 

30. 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. Where does the ball land relative to the car?

a) behind the car

Neglecting air resistance, if the car kept the same velocity, we would expect the ball to fall back into the car. But the car speeds up so it is in front of where it would have been with constant velocity. But the ball continues along its same path, coming back to where the car would have been. Therefore, the ball falls behind the car.

b) back into the car

c) in front of the car

 

31. 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.

 

32. Galileo

a) may be called the Father of Modern Electricity.

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.

 

33. 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.

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)

 

34. 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.

 

35. 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.

 

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

a) zero

b) 25 N

c) 50 N

d) 100 N

 

37. 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

 

38. In the sketch above, what value will the scale read if the little girl's weight is 5 newtons.

a) 2.5 N

The girl's weight of 5 N is supported twice by the tension in the rope -- once at her right hand and once at her left hand. Each force acting up, then, is 2.5 N.

[ Incidently, 5 newtons is far too small to be a realistic weight for a child. A mass of 25 kg would correspond to a weight of 55 lbs so that might be realistic or reasonable. A mass of 25 kg has a weight of 250 N. The numbers in this question are unrealistic but the ideas are still valid ].

b) 5.0 N

c) 10.0 N

d) 15.0 N

 

39. The four fundamental forces are

a) gravity, friction, electricity, and atomic

b) gravity, electromagnetic, strong nuclear, and weak nuclear

c) gravity, strong electric, weak electric, and atomic

d) gravity, friction, air resistance, and atomic

 

40. Aristotle and Plato thought

a) the Sun was at the center of the Universe

b) Earth revolved around the Sun

c) Earth was at the center of the Universe

d) the Sun revolved around the Moon