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 four-person bobsled $(total mass = 630 kg)$ comes down a straightaway at the start of a bobsled run. The straightaway is 80.0 m long and is inclined at a constant angle of $10.2 °$ with the horizontal. Assume that the combined effects of friction and air drag produce on the bobsled a constant force of 62.0 N that acts parallel to the incline and up the incline. Answer the following questions to three significant digits.
(a) If the speed of the bobsled at the start of the run is 6.20 m/s, how long does the bobsled take to come down the straightaway?
(b) Suppose the crew is able to reduce the effects of friction and air drag to 42.0 N. For the same initial velocity, how long does the bobsled now take to come down the straightaway?

$a) 6.80 s b) 6.76 s$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

$Total mass (m) = 630 kg Lenght (s) = 80.0 m and is inclined at a constant angle of 10.2 ° with the horizontal . Force (f) = 62.0 N Initial velocity is, u = 6.20 m / s$

Step 2: Understanding the concept

The problem deals with Newton’s second law of motion. It tells us that the acceleration a of an object is affected by the net force F acting upon the object and the mass of m the object.

Formula:

F = ma

Step 3: a)Calculate how long the bobsled takes to come down the straightaway if the speed of the bobsled at the start of the run is 6.20 m/s

The component of the weight along the incline (with downhill understood as the positive direction) is,

$m g \sin θ$

Where m is the mass and is $θ$ the angle.

We can write the balance force equation as,

$m g \sin θ - f = m a$

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

$630 \times 9.8 \times \sin 10.2 ° - 62 = 630 \times a a = 1.937 m / s^{2} a = 1.64 m / s^{2}$

We know that from the equation of motion, we can write the expression for distance as,

$s = u t + 1 / 2 a t^{2}$

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

$80.0 m = (6.20 m / s) t + (1 / 2) (1.64 m / s^{2}) t^{2}$

The above equation is a quadratic equation of t; we can find the root as,

t = 6.80 s

Thus, the bobsled takes 6.80 s to come down straightaway.

Step 4: b) Calculate how long the bobsled now takes to come down the straightaway for the same initial velocity if the effects of friction and air drag is reduced to 42.0 N

$Force (f) = 42.0 N$

We can write the balance force equation as,

$m g \sin θ - f = m a$

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

$630 \times 9.8 \times \sin 10.2 ° - 42 = 630 \times a a = 1.66 m / s^{2}$

We know that from the equation of motion, we can write the expression for distance as,

$s = u t + 1 / 2 a t^{2}$

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

$80.0 m = (6.20 m / s) t + (1 / 2) (1.66 m / s^{2}) t^{2}$

The above equation is a quadratic equation of t; we can find the root as,

t = 6.76 s

Thus, the bobsled takes 6.76 s to come down the straightaway.

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 how long the bobsled takes to come down the straightaway if the speed of the bobsled at the start of the run is 6.20 m/s

Step 4: b) Calculate how long the bobsled now takes to come down the straightaway for the same initial velocity if the effects of friction and air drag is reduced to 42.0 N

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 how long the bobsled takes to come down the straightaway if the speed of the bobsled at the start of the run is 6.20 m/s

Step 4: b) Calculate how long the bobsled now takes to come down the straightaway for the same initial velocity if the effects of friction and air drag is reduced to 42.0 N

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