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 machine pulls a 40 kg trunk 2.0 m up a $40 °$ ramp at a constant velocity, with the machine’s force on the trunk directed parallel to the ramp. The coefficient of kinetic friction between the trunk and the ramp is 0.40 . What are (a) the work done on the trunk by the machine’s force and (b) the increase in thermal energy of the trunk and the ramp?

The work done on the trunk by the machine’s force is 744 J
The increase in thermal energy of the trunk and the ramp is 240.2 J

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data

The mass of the trunk is, m = 40 kg

The distance by which the trunk is pulled up, x = 2.0 m

The angle of inclination is, $θ = 40 °$

The coefficient of kinetic friction is, $μ_{k} = 0.40$

Step 2: Understanding the concept of energy and force

Using the equation for the net force, we can find the force due to the machine. From this force and displacement, we can find the work done by the machine. Using the frictional force, we can find the thermal energy generated.

Formulae:

Force due to Newton’s second law, F = ma (1)

The work done by the body, W = Fdcos $θ$ (2)

Step 3: a) Calculation of the work done on the trunk

We can resolve the gravitational force into its component along the incline and normal to the incline, we have and, respectively.

Using these components in equation (2), we get that

$F_{m} - mgsinθ - μ_{k} mgcosθ = ma$

The net acceleration is zero, so we can write the force as:

$F_{m} = mgsinθ + μ_{k} mgcosθ = 40 kg \times 9.8 m / s^{2} \times (\sin 40 °) + 0.40 \times kg \times 9.8 m / s^{2} \times (\cos 40 °) = 251.9 kg . m / s^{2} + 120.1 kg . m / s^{2} = 372 kg . m / s^{2} (\frac{1 N}{1 kg . m / s^{2}})$

Thus, work done by the machine can be given as:

$W = F_{m} \times d = 372 N \times 2 m = 744 N . m (\frac{1 J}{1 N . m}) = 744 J$

Hence, the value of the work done is 744J.

Step 4: b) Calculation of the increased thermal energy

The force due to friction is given as:

$F_{f} = μ_{k} mgcosθ$

So the thermal energy generated is equal to the work done by the frictional force, which is given using equation (2) as:

${WD}_{th} = μ_{k} mgcosθ \times d = 0.40 \times 40 kg \times 9.8 m / s^{2} \times \cos 40 ° \times 2.0 m = 240.2 kg . m / s^{2} (\frac{1 J}{1 kg . m / s^{2}}) = 240.2 J$

Hence, the value of the increase in thermal energy is 240.2 J .

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: The given data

Step 2: Understanding the concept of energy and force

Step 3: a) Calculation of the work done on the trunk

Step 4: b) Calculation of the increased thermal energy

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: The given data

Step 2: Understanding the concept of energy and force

Step 3: a) Calculation of the work done on the trunk

Step 4: b) Calculation of the increased thermal energy

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

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