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Physics Principle and Problems

Paul W. Zitzewitz, Todd George Elliott, David G. Haase

Chapter 5

Forces in Two Dimensions - all with Video Answers

Educators

Section 1

Vectors

00:34

Problem 1

A car is driven $125.0 \mathrm{km}$ due west, then $65.0 \mathrm{km}$ due south. What is the magnitude of its displacement? Solve this problem both graphically and mathematically, and check your answers against each other.

Mayukh Banik
Mayukh Banik
Numerade Educator
00:39

Problem 2

Two shoppers walk from the door of the mall to their car, which is 250.0 m down a lane of cars, and then turn $90^{\circ}$ to the right and walk an additional $60.0 \mathrm{m} .$ What is the magnitude of the displacement of the shoppers' car from the mall door? Solve this problem both graphically and mathematically, and check your answers against each other.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:29

Problem 3

A hiker walks $4.5 \mathrm{km}$ in one direction, then makes a $45^{\circ}$ turn to the right and walks another $6.4 \mathrm{km} .$ What is the magnitude of her displacement?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:01

Problem 4

An ant is crawling on the sidewalk. At one moment, it is moving south a distance of $5.0 \mathrm{mm}$. It then turns southwest and crawls $4.0 \mathrm{mm}$. What is the magnitude of the ant's displacement?

Mukesh Devi
Mukesh Devi
Numerade Educator
02:55

Problem 5

Algebraically. You may also choose to solve some of them graphically to check your answers.
Sudhir walks $0.40 \mathrm{km}$ in a direction $60.0^{\circ}$ west of north, then goes $0.50 \mathrm{km}$ due west. What is his displacement?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:54

Problem 6

Algebraically. You may also choose to solve some of them graphically to check your answers.
Afua and Chrissy are going to sleep overnight in their tree house and are using some ropes to pull up a box containing their pillows and blankets, which have a total mass of $3.20 \mathrm{kg} .$ The girls stand on different branches, as shown in Figure $5-6,$ and pull at the angles and with the forces indicated. Find the $x$ - and $y$ -components of the net force on the box. Hint: Draw a free-body diagram so that you do not leave out a force. (FIGURE CAN'T COPY)

Mayukh Banik
Mayukh Banik
Numerade Educator
00:36

Problem 7

Algebraically. You may also choose to solve some of them graphically to check your answers.
You first walk $8.0 \mathrm{km}$ north from home, then walk east until your displacement from home is $10.0 \mathrm{km} .$ How far east did you walk?

Mayukh Banik
Mayukh Banik
Numerade Educator
00:52

Problem 8

Algebraically. You may also choose to solve some of them graphically to check your answers.
A child's swing is held up by two ropes tied to a tree branch that hangs $13.0^{\circ}$ from the vertical. If the tension in each rope is $2.28 \mathrm{N},$ what is the combined force (magnitude and direction) of the two ropes on the swing?

Mayukh Banik
Mayukh Banik
Numerade Educator
00:33

Problem 9

Algebraically. You may also choose to solve some of them graphically to check your answers.
Could a vector ever be shorter than one of its components? Equal in length to one of its components? Explain.

Mayukh Banik
Mayukh Banik
Numerade Educator
00:31

Problem 10

Algebraically. You may also choose to solve some of them graphically to check your answers.
In a coordinate system in which the $x$ -axis is east, for what range of angles is the $x$ -component positive? For what range is it negative?

Mayukh Banik
Mayukh Banik
Numerade Educator
00:37

Problem 11

Distance v. Displacement Is the distance that you walk equal to the magnitude of your displacement? Give an example that supports your conclusion.

Mayukh Banik
Mayukh Banik
Numerade Educator
00:35

Problem 12

Vector Difference Subtract vector $\boldsymbol{K}$ from vector L, shown in Figure $5-7$. (FIGURE CAN'T COPY)

Mayukh Banik
Mayukh Banik
Numerade Educator
00:31

Problem 13

Components Find the components of vector $\boldsymbol{M}$ shown in Figure $5-7$. (FIGURE CAN'T COPY)

Mayukh Banik
Mayukh Banik
Numerade Educator
00:59

Problem 14

Vector Sum Find the sum of the three vectors shown in Figure $5-7$. (FIGURE CAN'T COPY)

Mayukh Banik
Mayukh Banik
Numerade Educator
00:50

Problem 15

Commutative Operations The order in which vectors are added does not matter. Mathematicians say that vector addition is commutative. Which ordinary arithmetic operations are commutative? Which are not?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:06

Problem 16

Critical Thinking A box is moved through one displacement and then through a second displacement. The magnitudes of the two displacements are unequal. Could the displacements have directions such that the resultant displacement is zero? Suppose the box was moved through three displacements of unequal magnitude. Could the resultant displacement be zero? Support your conclusion with a diagram.

Mayukh Banik
Mayukh Banik
Numerade Educator