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 luge and its rider, with a total mass of 85 kg, emerge from a downhill track onto a horizontal straight track with an initial speed of 37 m/s. If a force slows them to a stop at a constant rate of 2.0 m/s², (a) what magnitude F is required for the force, (b) what distance d do they travel while slowing, and (c) what work W is done on them by the force? What are (d) f , (e) d , and (f) W if they, instead, slow at 4.0 m/s² ?

The magnitude of Force when $a = 2.0 m / s^{2}$ is $1.7 \times 10^{2} N$ .
Distance traveled before coming to a stop when $a = 2.0 \frac{m}{s^{2}}$ is $3.4 \times 10^{2} m$ .
Work done by the force on the rider when $a = 2.0 m / s^{2}$ is $- 5.8 \times 10^{4} J$ .
The magnitude of force when $a = 4.0 m / s^{2}$ is $3.4 \times 10^{2} N$ .
Distance traveled before coming to a stop when $a = 4.0 m / s^{2}$ is $1.7 \times 10^{2} m$ .
Work done by the force on the rider when $a = 4.0 m / s^{2}$ is $- 5.8 \times 10^{4} J$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

i) Mass of the rider is, m=85 kg.

ii) Initial velocity is, $v_{i} = 37 \frac{m}{s}$ .

iii) Acceleration is, $a_{1} = 2.0 \frac{m}{s^{2}}$ .

Step 2: Understanding the concept

As we are given the acceleration and mass of the rider, using Newton’s 2^nd law, we can find the force acting on them. As we know the initial velocity, final velocity, and acceleration, we can find the distance traveled. As we get the force and displacement, we can find the work done by the force. Using the same procedure, we can find the force, distance, and work done when the rider has an acceleration of $a = 4.0 \frac{m}{s^{2}}$ .

Step 3: (a) Calculate the magnitude of F required if it slows them to a stop at a constant rate of 2.0 m/s2

The relationship between force exerted on a particle mass m of the particle and acceleration a of the particle can be written as,

$F = ma$ (1)

Substitute the values in the given expression, and we get the magnitude of the force as,

$|\vec{F}| = |85 \times (- 2.0)| F = |- 1.7 \times 10^{2} N| F = 1.7 \times 10^{2} N$

Thus, the magnitude of Force when $a = 2.0 m / s^{2}$ is $1.7 \times 10^{2} N$ .

Step 4: (b) Calculate the distance d that they travel while slowing down

Newton's law of motion, we can write the below expression and calculate the traveled distance x as,

$v_{f}^{2} = v_{i}^{2} + 2 ax$ (2)

As the rider is coming to a stop, so we can say that the final velocity is, $v_{f} = 0 \frac{m}{s}$

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

$\begin{array}{rcl} 0 & = & 37^{2} - (2 \times 2 \times d) \\ 37^{2} & = & 4 d \\ d & = & \frac{1369}{4} \\ d & = & 3.4 \times 10^{2} m \end{array}$

Thus, the distance traveled before coming to a stop when $a = 2.0 \frac{m}{s^{2}}$ is $3.4 \times 10^{2} m$ .

Step 5: (c) Calculate work done on them by the force

If the force F is exerted on a body and it traveled distance d, then the expression for the work done can be expressed as,

$W = Fd$ (3)

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

$W = (- 1.7 \times 10^{2}) \times (3.4 \times 10^{2}) W = - 5.8 \times 10^{4} J$

Thus, work done by the force on the rider when $a = 2.0 m / s^{2}$ is $- 5.8 \times 10^{4} J$ .

Step 6: (d) Calculate the magnitude of F required if it slows them to a stop at a constant rate of 4.0 m/s2

Given that,

$a = 4.0 \frac{m}{s^{2}}$

From equation 1, we can calculate the magnitude of the force as,

$|\vec{F}| = |85 \times (- 4.0)| F = |(- 3.4 \times 10^{2} N)| F = 3.4 \times 10^{2} N$

Thus, the magnitude of force when data-custom-editor="chemistry" $a = 4.0 m / s^{2}$ is $3.4 \times 10^{2} N$ .

Step 7: (e) Calculate the distance d that they travel while slowing down

Given that,

$a = 4.0 \frac{m}{s^{2}}$

From equation 2, we can calculate the distance in this case as,

$\begin{array}{rcl} 0 & = & 37^{2} - (2 \times 4 \times d) \\ 37^{2} & = & 8 d \\ d & = & \frac{1369}{8} \\ d & = & 1.7 \times 10^{2} m \end{array}$

Thus, the distance traveled before coming to a stop when $a = 4.0 m / s^{2}$ is $1.7 \times 10^{2} m$

Step 8: (f) Calculate work done on them by the force

From equation 3, we can calculate the work done as,

$W = (- 3.4 \times 10^{2}) \times (1.7 \times 10^{2}) W = - 5.8 \times 10^{4} J$

Thus, work done by the force on the rider when data-custom-editor="chemistry" $a = 4.0 m / s^{2}$ is $- 5.8 \times 10^{4} J$ .

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: Given data

Step 2: Understanding the concept

Step 3: (a) Calculate the magnitude of F required if it slows them to a stop at a constant rate of 2.0 m/s2

Step 4: (b) Calculate the distance d that they travel while slowing down

Step 5: (c) Calculate work done on them by the force

Step 6: (d) Calculate the magnitude of F required if it slows them to a stop at a constant rate of 4.0 m/s2

Step 7: (e) Calculate the distance d that they travel while slowing down

Step 8: (f) Calculate work done on them by the force

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: (a) Calculate the magnitude of F required if it slows them to a stop at a constant rate of 2.0 m/s2

Step 4: (b) Calculate the distance d that they travel while slowing down

Step 5: (c) Calculate work done on them by the force

Step 6: (d) Calculate the magnitude of F required if it slows them to a stop at a constant rate of 4.0 m/s2

Step 7: (e) Calculate the distance d that they travel while slowing down

Step 8: (f) Calculate work done on them by the force

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