Creative Physics Problems for Physics with Calculus: Mechanics 1

141 Pages·2.271 MB·English

by  Chris McCullen

Creative Physics Problems – Chris McMullen, Ph.D.

Creative Physics Problems
For Physics with Calculus
Vol. 1: Mechanics

Chris McMullen, Ph.D.

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Volume 1: Mechanics

Creative Physics Problems for Physics with Calculus
Volume 1: Mechanics

Copyright (c) 2009 Chris McMullen

All rights reserved. This includes the right to reproduce any portion of this book in any form. However,
teachers who purchase one copy of this book, or borrow one physical copy from a library, may make and
distribute photocopies of selected pages for instructional purposes for their own classes only.

www.faculty.lsmsa.edu/CMcMullen

Custom Books

Textbooks / science / physics

ISBN: 1442190957

EAN-13: 9781442190955
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Creative Physics Problems – Chris McMullen, Ph.D.

Contents

1 One-Dimensional Motion 4
2 Projectile Motion and Vectors 14
Review 1: Motion 25
3 Newton’s Laws of Motion 34
4 Uniform Circular Motion 48
Review 2: Newton’s Laws 54
5 Conservation of Energy 64
6 Systems of Objects 75
Review 3: Conservation of Energy and Momentum 86
7 Rotation 95
8 Fluids (One Problem) 114
Review 4: Rotation 115
Final Review: Mechanics 119
Answers to Selected Problems 109

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Volume 1: Mechanics

1 One-Dimensional Motion

Note: An asterisk (*) designates a problem that does not have an answer at the back of the book.

Note: Problems near the surface of the earth involve gravitational acceleration equal to 9.81 m/s2.
However, in some of the answers, this value was rounded to 10 m/s2 – usually, for problems where the
numbers would then work out nicely without the need of a calculator.

*1. Monkey Units I. Below are some conversions between Monkey Units and more common units.
1 banana = 8.34 inches 1 coconut = 9.42 cm
1 pound = 6.34 peels 1 eek = 0.79 seconds
(A) How tall is a monkey in cm whose height is 5.2 bananas? (B) How much does a 150-lb. person weigh
in peels? (C) How many coconuts are there in one banana? (D) What is the area of an 8.5”  11” sheet
of paper in coconuts2? (E) Express 9.81 m/s2 in bananas/eek2.

22
 0
g
*2. Monkey Units II. What are the SI units of the monkey symbol defined as ?

3. Physics Makes You Run Around in Circles. Two monkeys jog around a circular track with a length of
one kilometer. One monkey jogs clockwise at a rate of 5 m/s, while his sister jogs counterclockwise at a
rate of 8 m/s. They begin from the same position. (A) How much time passes before they first meet?
(B) How many laps has the sister completed when her brother completes his 15th lap? (C) After one
minute, how much further has the sister traveled compared to her brother? (D) What are the
components of the net displacement of the monkeys when they first meet?

4. Going Bananas! A monkey jogs around the track illustrated below. The bottom arc is semicircular
with 50-m radius. The monkey completes the lap in 40 seconds. The monkey runs:

(i) at a constant speed of 10 m/s from A to B along the semicircular arc
(ii) at a different constant speed from B to A along the straight section.

A B

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Creative Physics Problems – Chris McMullen, Ph.D.

(A) What is the total distance traveled by the monkey in trip (i)? (B) What is the net displacement of the
monkey in trip (i)? (C) How fast did the monkey travel in trip (ii)? (D) What is the average speed of the
monkey for the whole lap? (E) What is the magnitude of the average velocity of the monkey for the
whole lap?

*5. Monkey Motion. A monkey runs 120 m east at some constant speed, then runs 160 m north at a
constant speed of 8 m/s. The whole trip takes one minute. (A) What is the net displacement of the
monkey? (B) What is the average speed of the monkey? (C) How fast did the monkey run to the east?
(D) What is the average velocity of the monkey?

6. Monkey Climbing. A monkey’s velocity is plotted as a function of time below.

10 A
8 ●
6
4 ● B
2
v (m/s) 0

-2
-4 C ●
-6
-8

-10
0 1 2 3 4 5 6 7 8
t (s)

(A) Find the velocity of the monkey at point B. (B) Find the acceleration of the monkey at point C. (C) At
what time is the velocity of the monkey equal to zero? (D) For what time interval(s) is the monkey
moving in the negative x direction? (E) For what time interval(s) is the acceleration of the monkey
negative? (F) What is the maximum speed of the monkey? (G) Find the total distance traveled by the
monkey. (H) Find the net displacement of the monkey. (I) What is the average speed of the monkey?
(J) What is the average velocity of the monkey?

7. Wild Monkeys I. The position of a monkey is illustrated below as a function of time.
x(m)
8
6
4
2
0
-2
-4
-6
-8
0 3 6 9 12 15 18 21 24 27 30
t(s)

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Volume 1: Mechanics

(A) What is the monkey’s net displacement? (B) What is the total distance traveled? (C) What is the
monkey’s initial velocity? (D) What is the monkey’s final velocity? (E) Where is the monkey at s?
(F) When is the monkey moving fastest?

8. Three Little Piggies. The 1st Little Piggy, who went to the market:
40

32

24

16

8
x(m) 0

-8

-16

-24

-32
-40
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
 
t s
Note: Clearly show all work. Explain how you obtain your answers.

(A) What is the net displacement of the 1st little piggy? (B) What is the average speed of the 1st little
piggy? (C) For how many seconds (total) is the 1st little piggy moving backwards? (D) For what time
interval(s) is the 1st little piggy moving with uniform velocity? (E) What is the final velocity of the 1st little
piggy? (F) What is the maximum speed of the 1st little piggy?

The 2nd Little Piggy, who chased the sun:
10

8

6

4

2
(m/s)
0

-2

-4

-6

-8
-10
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60
t(s)

(G) At what time(s) is the velocity of the 2nd little piggy equal to zero? (H) At what time(s) is the
acceleration of the 2nd little piggy equal to zero? (I) What is the maximum speed of the 2nd little piggy?
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Creative Physics Problems – Chris McMullen, Ph.D.

(J) What is the maximum acceleration of the 2nd little piggy? (K) What is the total distance traveled by
the 2nd little piggy? (L) What is the average velocity of the 2nd little piggy?

The 3rd Little Piggy, who went Weeeeeee! all the way home:
2.5

2

1.5

1

0.5
a(m/s2)
0
-0.5

-1

-1.5

-2
-2.5
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
t(s)
Note: The initial velocity of the 3rd little piggy is 10 m/s.

(M) For what time interval(s) does the 3rd little piggy travel with negative acceleration? (N) For what
time interval(s) does the 3rd little piggy travel backwards? (O) For what time interval(s) does the 3rd little
piggy travel with uniform acceleration? (P) What is the velocity of the 3rd little piggy at t 8 s? (Q) At
what time(s) is the acceleration of the 3rd little piggy equal to zero? (R) What is the acceleration of the
3rd little piggy at t 25 s? (S) Make a sketch of acceleration as a function of time for the 2nd little piggy.

*9. Wild Monkeys. For each graph of a wild monkey illustrated below, sketch a curve of velocity as a
function of time. Take care drawing significant features.
20
15
10
5
x(m)
0
-5
-10
-15
-20
0 3 6 9 12 15 18 21 24 27 30
t(s)

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Volume 1: Mechanics

20
15
10
5
a(m/s2)
0
-5
-10
-15
-20
0 3 6 9 12 15 18 21 24 27 30
t(s)

*10. Little Piggy. Sketch the time-dependence of displacement, velocity, and acceleration for a
uniformly accelerated little piggy (in one dimension) with x 0,  0, and a0.
0 0

*11. Average Monkey. An average monkey runs from home to the banana store at a constant speed of
3 m/s. The average monkey then returns home at a constant speed of 5 m/s. (A) Conceptually explain
why the average monkey’s average speed is not 4 m/s for the roundtrip. Should the average speed be
greater or less than 4 m/s? Explain. (B) Compute the average monkey’s average speed for the
roundtrip.

12. Monkey Skater I. A monkey on roller skates has a velocity given by

(t)(t)2 

where  and  are constants. In their appropriate SI units,  = ½ and  = 2. The monkey skates for 8
seconds with an initial velocity of -10 m/s. (A) What are the SI units of  and ? (B) Solve for . (C)
What is the maximum speed of the monkey? (D) What is the acceleration of the monkey after skating
for 4 seconds? (E) How far does the monkey travel before changing direction? (F) What is the average
velocity of the monkey? (G) What is the average speed of the monkey?

13. Monkey Skater II. A monkey on roller skates has an acceleration given by

a(t) t

where  = 15 in SI units. The monkey skates for 4 s with an initial velocity of -40 m/s. (A) What are the
SI units of ? (B) What is the final velocity of the monkey? (C) What is the average velocity of the
monkey?

*14. Lazy Monkey. A monkey is so lazy that instead of actually running around, he just imagines
running around with the following velocity: (t)3(2t)2 where SI units have been suppressed for
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Creative Physics Problems – Chris McMullen, Ph.D.

convenience. The monkey imagines his motion to begin at t 0 and end at t 6 seconds. (A) What
acceleration does the monkey imagine having at t 4 seconds? (B) What is the net displacement for
the monkey’s imagined trip? (C) At what time(s), if any, does the monkey imagine running 27 m/s?

t2 7
*15. Scaredy Monk. A monkey runs with a velocity of (t)  after a black cat sneaks up on
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him and meows. SI units have been suppressed for convenience, but you may not take that luxury in
your answers. (A) What is the net displacement of the monkey after 4 seconds? (B) What is the
acceleration of the monkey at t 13 sec?

16. Monkey Wish. A monkey makes a wish (for more bananas, of course!) as she drops a banana into a
wishing well. She hears the splash of the banana two and one-half seconds later. (Neglect the time it
takes for the sound to travel to her ears.) (A) How deep is the well? (B) What was the final speed of the
banana?

17. Monkey Jordan. Many monkeys claim that the great Monkey Jordan can jump with a hangtime of 2
seconds. How high would Monkey Jordan need to jump to have such a hangtime? Is this realistic?

18. Banana’s Revenge. A 30-kg banana throws a 20-kg monkey upward with a speed of 25 m/s from
the roof of a 50-m tall building. (A) How long is the monkey in the air? (B) What is the final speed of the
monkey? (C) What is the maximum height of the monkey in the air (relative to the ground)?

19. Ceiling. A ball is thrown straight upward at a speed of 40 m/s. It strikes the ceiling 3 seconds later.
About how high is the ceiling? (Can this be a typical room?)

*20. Stopping on a Dime. A monkey driving a bananamobile 40 m/s spots a baby monkey crossing the
street 100 m ahead. The monkey uniformly decelerates, stopping just in time. For how much time does
the monkey decelerate?

*21. Jumping for Joy. A monkey leaps upward from a trampoline with an initial speed of 30 m/s. How
high does the monkey leap?

*22. Chutes and Ladders. A monkey slides down a 40-m long incline from rest, reaching the bottom in
four seconds. What is his acceleration?

*23. Banana Split. A monkey driving a bananamobile spots a banana split 200 m ahead on the highway.
The monkey uniformly decelerates for 5 seconds, stopping just in time to avoid squashing the banana
split. Find (A) the initial velocity and (B) acceleration of the bananamobile.

24. Wait a Minute! A knight rides 15 m/s on horseback to rescue a princess when he realizes that he
forgot to brush his teeth in the morning. What is his stopping distance if he uniformly decelerates at a
rate of 2.0 m/s2?

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Volume 1: Mechanics

25. Towering Knight. A knight jumps on a trampoline to rescue a princess from the highest tower of a
castle. If his maximum height is 60 m, find his (A) speed and (B) jump time when his height is 40 m on
his return down.

26. Stairway to Heaven. A princess runs upstairs to rescue a knight from a high tower. As she tires, she
uniformly decelerates at a rate of 0.2 m/s2. Five seconds later, her speed is 3.6 m/s. During these five
seconds, how many 20-cm tall stairs did she climb?

27. Court Jouster. The court jester is jousting with a pencil as his lance. He stands 200 m from his
opponent. From rest, he uniformly accelerates at a rate of 2.5 m/s2 as he approaches his fierce
opponent, who gallops at a constant rate of 10 m/s. (A) Where will they meet? (B) When will they
meet? (C) What is the speed of the court jester when they meet?

*28. Halfway Up. A chimpanzee throws a banana vertically upward at a speed of 30 m/s. How fast is
the banana moving when it is halfway up?

*29. Monkey Wrench. A monkey on the ground throws a 3-kg monkey wrench vertically upward. The
wrench is moving 15 m/s when it reaches 50% of its maximum altitude. (A) How long is the wrench is in
the air? (B) How high does the wrench rise? (C) How fast was the wrench thrown?

*30. Hot Pursuit. A police orangutan is driving 30 m/s when he spots a speeding monkey ahead. In
order to catch the speeding monkey, the police orangutan uniformly accelerates to 50 m/s over a
distance of 200 m. (A) Find the acceleration of the police orangutan. (B) How much time elapses during
this acceleration? (C) Once the police orangutan reaches 50 m/s, a monkey crosses the street, pushing
her baby carriage. The police orangutan uniformly decelerates for 100 m, just barely stopping in time.
For how much time does the police orangutan decelerate?

*31. Stress Reduction. A monkey ties a firecracker to his physics textbook and launches the textbook
straight upward with an initial speed of 40 m/s.1 The firecracker explodes six seconds after launch. (A)
How high is the textbook above the ground when the firecracker explodes? (B) What is the velocity of
the textbook just before the firecracker explodes? (C) What is the maximum height of the textbook
above the ground?

*32. Interception. You lean out of your second-story dorm window (10 meters above the ground) and
throw a ball upward with an initial speed of 30 m/s. Unfortunately, while the ball is returning downward
somebody in a room above leans out the window (35 meters above the ground) and intercepts it. (A)
How much time elapsed after the ball was thrown before it was intercepted? (B) What was the
maximum height of the ball above the ground?

33. Mighty Pen. To illustrate that the pen is mightier than the sword, a brave knight throws his sword
high up into the air. He patiently waits for its return, holding a pen up. After the sword is 10 m above
the ground on the way up, four seconds elapse before the sword is moving 15 m/s on the way down.
(A) Where is the sword when it is moving 15 m/s on the way down? (B) What are (i) the average velocity

1 Professional stunt monkey. Do not attempt.
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