Conceptual Physics

Chapter 3 Problems

Conceptual Problems

C.1 List three quantities that are represented by vectors.

C.2 Compare these two vectors: (5, 185°) and the negative of (5, 5°). Are they the same vector? Why or why not?

Yes No

C.3 An aircraft carrier sails northeast at a speed of 6.0 knots. Its velocity vector is v. What direction and speed would a ship with

velocity vector –v have?

knots i. Northwest

ii. Northeast

iii. Southwest

iv. Southeast

C.4 Can the same vector have different representations in polar notation that use different angles? Explain.

Yes No

C.5 A Boston cab driver picks up a passenger at Fenway Park, drops her off at the Fleet Center. Represent this displacement

with the vector D. What is the displacement vector from the Fleet Center to Fenway Park?

D 2 D 0 íD

C.6 Does the multiplication of a scalar and a vector display the commutative property? This property states that the order of

multiplication does not matter. So for example, if the multiplication of a scalar s and a vector r is commutative, then sr = rs for

all values of s and r.

Yes No

Section Problems

Section 0 - Introduction

0.1 Use the simulation in the interactive problem in this section to answer the following questions. Assume that the simulation is
reset before each part and give each answer in the form (x,y). (a) What is the displacement to Ed's Fuel Depot? (b) What is
the displacement to Joe's Diner? (c) What is the displacement to Silver's Gym?
(a) ( km, km)
(b) ( km, km)
(c) ( km, km)

Section 1 - Scalars

1.1 The Earth has a mass of 5.97×10^24 kg. The Earth's Moon has a mass of 7.35×10^22 kg. How many Moons would it take to

have the same mass as the Earth?

1.2 The volume of the Earth's oceans is approximately 1.4×10^18 m^3. The Earth's radius is 6.4×10^6 m. What percentage of the

Earth, by volume, is ocean?

%

1.3 Density is calculated by dividing the mass of an object by its volume. The Sun has a mass of 1.99×10^30 kg and a radius of

6.96×10^8 m. What is the average density of the Sun?

kg/m^3

Section 3 - Polar notation

3.1 The tugboat Lawowa is returning to port for the day. It has a speed of 7.00 knots. The heading to the Lawowa's port is 31.0°

west of north. If due east is 0°, what is the tug's heading as a vector in polar notation?

( knots, °)

3.2 An analog clock has stopped. Its hands are stuck displaying the time of 10 o'clock. The hour hand is 5.0 centimeters long,

and the minute hand is 11 centimeters long. Write the position vector of the tip of the hour hand, in polar notation. Consider

3 o'clock to be 0°, and assume that the center of the clock is the origin.

( cm, °)

Copyright 2007 Kinetic Books Co. Chapter 3 Problems^61