Products
Rewards 
from HOLOOLY

We are determined to provide the latest solutions related to all subjects FREE of charge!

Please sign up to our reward program to support us in return and take advantage of the incredible listed offers.

Enjoy Limited offers, deals & Discounts by signing up to Holooly Rewards Program

HOLOOLY 
BUSINESS MANAGER

Advertise your business, and reach millions of students around the world.

HOLOOLY 
TABLES

All the data tables that you may search for.

HOLOOLY 
ARABIA

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

HOLOOLY 
TEXTBOOKS

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

HOLOOLY 
HELP DESK

Need Help? We got you covered.

Chapter 1

Q. 3.4

A force of 4 N has the direction π/3. What is the work done in moving an object from the point (1, 2) to the point (5, 4), where distances are measured in meters?

Step-by-Step

Verified Solution

A unit vector with direction \pi / 3 is given by \mathbf{u}=(\cos \pi / 3) \mathbf{i}+(\sin \pi / 3) \mathbf{j}=(1 / 2) \mathbf{i}+(\sqrt{3} / 2) \mathbf{j}. Thus \mathbf{F}=4 \mathbf{u}=2 \mathbf{i}+2 \sqrt{3} \mathbf{j}. The displacement vector \mathbf{d} is given by (5-1) \mathbf{i}+(4-2) \mathbf{j}=4 \mathbf{i}+2 \mathbf{j}. Thus

W=\mathbf{F} \cdot \mathbf{d}=(2 \mathbf{i}+2 \sqrt{3} \mathbf{j}) \cdot(4 \mathbf{i}+2 \mathbf{j})=(8+4 \sqrt{3}) \approx 14.93 \mathrm{~N} \cdot \mathrm{m}

The component of \mathbf{F} in the direction of motion is sketched in Figure 5 .