# Metric System Problem: 1.2.6 The diameter of an aluminum atom is about 0.24 nm, and the nuclear diameter

Metric System

Problem: 1.2.6

The diameter of an aluminum atom is

about 0.24 nm, and the nuclear diameter is about 7.2 fm

(femtometer = 10−15 meter). (a) If the atom’s diameter

were expanded to the length of an American football field (91.44 m) and the

nuclear diameter expanded proportionally, what would be the nuclear diameter in

meters? (b) Is the saying that “the atom is mostly empty space” confirmed

by these figures?

(a) m

(b) Yes No

Problem: 1.8.2

Freefall acceleration g is

the acceleration due to gravity. It equals 9.80 meters per second squared near

the Earth’s surface. (a) What does it equal in feet per second squared? (b) In

miles per second squared? (c) In miles per hour squared?

(a) ft/s2

(b) mi/s2

(c) mi/h2

Problem: 1.8.4

You are on the phone with a friend

in Greece, who tells you that he has just caught a fish L cm long in the

Mediterranean Sea. Assuming he is telling the truth, what is the length of the

fish in inches?

in

Problem: 1.8.7

Mercury orbits the Sun at a mean

distance of 57,900,000 kilometers. (a) What is this distance in meters? Use

scientific notation to express your answer and state it with three significant

figures. (b) Pluto orbits at a mean distance of 5.91×1012 meters from the Sun. What is this distance in kilometers?

(a) m

(b)

Problem:

1.8.8

In 2003, Bill Gates was worth 40.7

billion dollars. (a) Express this figure in dollars in scientific notation. (b)

Assume a dollar is worth 2,060 Italian lire. State Bill Gates’s net worth in

lire in scientific notation.

(a) dollars

(b) lire

Dimensional Analysis

Problem: 1.10.2

The dimensions for force are the

product of mass and length, divided by time squared. Newton’s law of

gravitation states that the gravitational force between two objects equals a

constant, G, times the product of the mass of each object, divided by

the square of the distance between them. What must the dimensions of the

constant be?

L3/MT2

L2/T3

M2T

Problem: 1.10.4

The kinetic energy of an object is

given by the equation KE = (1/2)mv2, where m is mass and v is speed, with

dimensions L/T. What are the dimensions of KE?

ML2/T2

L2/T2

LM/T

Problem: 1.11.2

Evaluate (5.7×106 kg) × (6.3×10−2

m/s2) and express the answer in scientific notation.

kg·m/s2

Problem: 1.13.4

You have $1.14×104 in your checking account but must pay $3.30×103 in tuition. What is the balance in your checking account

after you pay your tuition? Express the answer in scientific notation.

dollars

Problem: 1.17.2

Suzy is holding her kite on a string

25.0 m long when the kite hits the top of a flagpole, which is f m

higher than her hands. Assuming that the string is taut and forms a straight

line, what is the horizontal distance from her hands to the flagpole?

m

Graphical Analysis of Motion

Problem: 2.C.8

Elaine wants to return a video she

rented at the video store, which is 5.0 kilometers away in the positive

direction. It takes her 10 minutes to drive to the store, 1.0 minute to deposit

the videotape, and 9.0 more minutes to drive home. What is her average velocity

for the entire trip?

m/s

Problem: 2.2.2

The school bus picks up Brian in

front of his house and takes him on a straight-line x km bus ride

to school in the positive direction. He walks home after school. If the front

of Brian’s house is the origin, (a) what is the position of the school, (b)

what is his displacement on the walk home, and (c) what is his displacement due

to the combination of the bus journey and his walk home?

(a) km

(b) km

(c) km

Problem: 2.3.2

A jogger is moving at a constant

velocity of +3.0 m/s directly towards a traffic light that is 100 meters

away. If the traffic light is at the origin, x = 0 m,

what is her position after running 20 seconds?

m

Problem: 2.4.4

You made a journey, and your displacement

was +95.0 km. Your initial velocity was +167 km/h and your final

velocity was −26.0 km/h. The journey took 43.0 minutes. What was your

average velocity in kilometers per hour?

km/h

Problem: 2.9.2

A graph of the velocity versus time

of a hockey puck is shown. Calculate the puck’s displacement from t = 1.0

s to t = 4.0 s.

m

Problem: 2.10.2

A sailboat is moving across the

water at 3.0 m/s. A gust of wind fills its sails and it accelerates at a

constant 2.0 m/s2. At the same instant, a motorboat

at rest starts its engines and accelerates at 4.0 m/s2. After 3.0 seconds have elapsed, find the velocity of (a)

the sailboat, and (b) the motorboat.

(a) m/s

(b) m/s

Problem: 2.11.5

The velocity versus time graph of an

ant is shown. What is the ant’s acceleration at (a) t = 1.0 s,

(b) t = 3.0 s, and (c) t = 5.0 s?

(a) cm/s2

(b) cm/s2

(c) cm/s2

Equation of Motion

Problem: 2.18.4

The brochure advertising a sports

car states that the car can be moving at 100.0 km/h, and stop in 37.19

meters. What is its average acceleration during a stop from that velocity?

Express your answer in m/s2. Consider the car’s initial

velocity to be a positive quantity.

m/s2

Problem: 2.23.2

A watermelon cannon fires a

watermelon vertically up into the air at a velocity of +v m/s,

starting from an initial position 1.20 meters above the ground. When the

watermelon reaches the peak of its flight, what is (a) its velocity, (b) its

acceleration, (c) the elapsed time, and (d) its height above the ground?

(a) m/s

(b) m/s2

(c) s

(d) m

Problem:

2.23.5

To determine freefall acceleration

on a moon with no atmosphere, you drop your handkerchief off the roof of a

baseball stadium there. The roof is 113 meters tall. The handkerchief reaches

the ground in 18.2 seconds. What is freefall acceleration on this moon? (State

the result as a positive quantity.)

m/s2

Problem: 2.23.6

You are a bungee jumping fanatic and

want to be the first bungee jumper on Jupiter. The length of your bungee cord

is 45.0 m. Freefall acceleration on Jupiter is 23.1 m/s2. What is the ratio of your speed on Jupiter to your speed

on Earth when you have dropped 45.0 m? Ignore the effects of air

resistance and assume that you start at rest.

Problem: 2.23.8

You stand near the edge of Half Dome

in Yosemite, reach your arm over the railing, and (thoughtlessly, since what

goes up does come down and there are people below) throw a rock upward at 8.00

m/s. Half Dome is 1460 meters high. How long does it take for the rock to reach

the ground? Ignore air resistance.

s

Vector Addition

Problem: 3.C.7

A small crab fishing boat travels

from Colon City on the Pacific Ocean, through the Panama Canal, to Panama City

on the Atlantic Ocean. A large cruise ship travels from Colon City to Panama

City by sailing all the way around the Cape Horn at the southern tip of South

America. Do these two voyages have equal displacement vectors?

Yes No

Problem:

3.4.3

Write the vectors labeled A, B

and C with rectangular coordinates.

(a) A = ( ,

)

(b) B = ( , )

(c) C = ( , )

Problem: 3.6.2

Solve for the unknown variables:

(a) (a, b) + (3, x) = (6, 7)

(b) (11, c) + (d, y) =(-12, −3)

(c) (5, 5) + (e, 4) = (2, f)

(d) (z, −3) − (5, g) = (h, 2)

(a) a = ; b

=

(b) c = ; d =

(c) e = ; f =

(d) g = ; h =

Addition of vectors

1)

Find the component of each of

the following vectors (show your work):

(6

points)

.0/msohtmlclip1/01/clip_image002.png”>

Answer

a)

x-component_______

y-component_______

Answer

b)

x-component_______

y-component_______

Answer

c)

x-component_______

y-component_______

2)

For the diagram below, identify

the resultant (A, B, or C) and complete the table

(3 points):

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.0/msohtmlclip1/01/clip_image004.png”>

Resultant

is : __________________

Vector

Equation: _________________

Direction

of Resultant (find angle)______________

3)

Given the vectors below, sketch

the following and draw the resultant (R). Do not draw a scaled vector diagram;

merely make a sketch. Label each vector. Clearly label the resultant (R).

(2 points)

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a)

Sketch for A + B + D (Clearly label

the Resultant)

b)

Sketch

B + C + E (Clearly label the Resultant)

4)

For the following vector addition diagrams, add the components of each vector

and draw the resultant. Then, using the

Pythagorean Theorem, find the magnitude and direction (angle) of the

resultant. Show your work.

b) (3 points)

a) (3 points)

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a) Sketch of resultant

Magnitude:______________

a)

Direction

(angle) __________

b) Sketch of resultant

Magnitude:______________

b)

Direction (angle) __________

c) (3 points)

.0/msohtmlclip1/01/clip_image010.png”>

Resultant

Magnitude

______________________

Direction

(angle) _______________________

Motion in two dimensions

Problem: 4.C.2

Two girls decide to jump off a

diving board. Katherine steps off the diving board. Anna runs straight off the

diving board so that her initial velocity is solely horizontal. They both leave

the diving board at the same time. Which one lands in the water first?

Problem: 4.1.2

In a visit to the nation’s capital,

a foreign head of state travels from (−3.0, −4.0) km to

(4.0, 7.0) km. She then travels with a displacement of (−5.0, a) km.

Calculate the her total displacement over the course of the trip.

( , ) km

Problem: 4.1.4

An irresolute boater drives south at

28 km/h for a half hour, pauses for 5 minutes, and then drives east for 45

minutes at 32 km/h. State his displacement vector in kilometers using

rectangular coordinates. Use the convention that north and east are positive.

( , ) km

Problem: 4.2.1

A golf ball is launched at a 37.0°

angle from the horizontal at an initial velocity of 48.6 m/s. State its

initial velocity in rectangular coordinates.

( , ) m/s

Problem: 4.2.2

The displacement vector for a 15.0

second interval of a jet airplane’s flight is (x, −2430) m.

(a) What is the magnitude of the average velocity? (b) At what angle, measured

from the positive x axis, did the airplane fly during this time

interval? Express the angle as a number between −180° and +180°

(a) m/s

(b) °

Problem: 4.7.1

A friend throws a baseball

horizontally. He releases it at a height of 2.0 m and it lands 21 m

from his front foot, which is directly below the point at which he released the

baseball. (a) How long was it in the air? (b) How fast did he throw it?

(a) s

(b) m/s

Problem: 4.7.2

A cannon mounted on a pirate ship

fires a cannonball at 125 m/s horizontally, at a height of 17.5 m

above the ocean surface. Ignore air resistance. (a) How much time elapses until

it splashes into the water? (b) How far from the ship does it land?

(a) s

(b) m

Problem: 4.7.4

A juggler throws a ball with an

initial horizontal velocity of +1.1 m/s and an initial vertical velocity

of +5.7 m/s. What is its acceleration at the top of its flight path? Make

sure to consider the sign when responding. Consider the upward direction as

positive.

m/s2

Interactive Problems

1. A clown in a circus is about to be

shot out of a cannon with a muzzle velocity of 15.2 m/s, aimed at 52.7° above

the horizontal. How far away should his fellow clowns position a net to ensure

that he lands unscathed? The net is at the same height as the mouth of the

cannon

Δx = m

2. A professional soccer player is 25.8

m from the goal, and kicks a hard shot from ground level. The ball hits the

crossbar on its way down, 2.44 m above the ground, 1.98 s after it was kicked.

What were the x and y components of the ball’s initial velocity? Take upward to

be the positive y direction.

vx = m/s

viy = m/s

Force and Newton’s Laws

Problem: 5.4.4

A dog on Earth weighs 136 N.

The same dog weighs 154 N on Neptune. What is the acceleration due to

gravity on Neptune?

m/s2

Problem: 5.5.2

A 0.125 kg frozen hamburger

patty has two forces acting on it that determine its horizontal motion. A

2.30 N force pushes it to the left, and a 0.800 N force pushes it to

the right. (a) Taking right to be positive, what is the net force acting on it?

(b) What is its acceleration?

(a) N

(b) m/s2

Problem:

5.5.4

The net force on a boat causes it to

accelerate at 1.55 m/s2. The mass of the boat is

215 kg. The same net force causes another boat to accelerate at

0.125 m/s2. (a) What is the mass of the second

boat? (b) One of the boats is now loaded on the other, and the same net force

is applied to this combined mass. What acceleration does it cause?

(a) kg

(b) m/s2

Problem: 5.11.4

A m kg box is resting on

a table. You push down on the box with a force of 8.00 N. What is the

magnitude of the normal force of the table on the block?

N

Problem: 5.12.2

During recess, Maria, who has mass

27.0 kg, hangs motionless on the monkey bars, with both hands gripping a

horizontal bar. Assume her arms are vertical and evenly support her body. What

is the tension in each of her arms?

N

Applications of Newton’s Laws

1. Use

the simulation in the interactive problem in Section 6.0 to answer the

following questions. (a) If F1 is

set to 12 N directly to the left, what should F2 be

set to so that the ball does not move when you press GO? (b) If F1 is

set to 10 N directly to the left, what should F2 be

set to so that the ball hits the target directly to the right of the ball? (c)

If F1 is set to 10 N straight up, what should F2 be

set to so that the ball hits the target that is up and to the right of the

ball?

(a) N,

(b) ,

(c) N,

2. A cat is stuck in a tree. You are designated with the job

to get it out, yet you do not want to climb the tree, because you may get stuck

as well. Instead you set up a pulley system. A rope (consider it massless) runs

from the seat you sit on over an ideal pulley and then to your hand. You pull

on the loose end of the rope with a force of 348 N. You weigh 612 N

and the seat you sit on weighs 16.0 N. (a) What is your acceleration? (b)

What force does the seat exert on you?

(a) m/s2

(b)

N

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