Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

Answers without the blur.

Just sign up for free and you're in.

Short Answer

A coin slides over a frictionless plane and across an xy coordinate system from the origin to a point with xy coordinates $(3.0 m, 4.0 m)$ while a constant force acts on it. The force has magnitude 2.0 N and is directed at a counterclockwise angle of $100^{°}$ from the positive direction of the x axis. How much work is done by the force on the coin during the displacement?

6.8 J of work is done by the force of 2.0 N on a coin during displacement.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

The initial position of the coin $= (0, 0)$ .

The final position of the coin $= (3.0 m, 4.0 m)$ .

Force is, $F = 20 N$ .

The angle at which the force is directed is, $θ = 100^{°}$ .

Step 2: Understanding the concept

Using the formula for work in terms of force and displacement, the work done in the x and y directions can be found separately. After this, we can add them to get the total work done by the force on the coin.

Formula:

$W = F ∆ x W_{total} = W_{x} + W_{y}$

Step 3: Calculate the work is done by the force on the coin during the displacement

A free body diagram can be drawn as,

From the above diagram, we can calculate the work done in the x direction as,

$W_{x} = F_{x} ∆ x$

Here, $∆ x$ is the displacement in the x direction.

Substitute the values in the above expression, and we get,

$W_{x} = (2.0 N \times \cos (100^{°})) \times (3.0 m - 0 m) W_{x} = - 1.01 N . m W_{x} = - 1.01 J$

From the above diagram, we can calculate the work done in the y direction as,

$W_{y} = F_{y} ∆ y$

Here, $∆ y$ is the displacement in the y direction.

Substitute the values in the above expression, and we get,

$W_{y} = (2 N \times \sin (100^{°})) \times (4.0 m - 0 m) W_{y} = 7.88 N . m W_{y} = 7.88 J$

Total work done will be,

$W = W_{x} + W_{y}$

Substitute the values in the above expression, and we get,

$W = - 1.01 J + 7.88 J W = 6.8 J$

6.8 J of work is done by the force of 2.0 N on a coin during displacement.

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Given data

Step 2: Understanding the concept

Step 3: Calculate the work is done by the force on the coin during the displacement

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Given data

Step 2: Understanding the concept

Step 3: Calculate the work is done by the force on the coin during the displacement

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Famous Physicists

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics