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 ski that is placed on snow will stick to the snow. However, when the ski is moved along the snow, the rubbing warms and partially melts the snow, reducing the coefficient of kinetic friction and promoting sliding. Waxing the ski makes it water repellent and reduces friction with the resulting layer of water. A magazine reports that a new type of plastic ski is especially water repellent and that, on a gentle 200 m slope in the Alps, a skier reduced his top-to-bottom time from 61 s with standard skis to 42 s with the new skis. Determine the magnitude of his average acceleration with (a) the standard skis and (b) the new skis. Assuming a $3.0 °$ slope, compute the coefficient of kinetic friction for (c) the standard skis and (d) the new skis.

$(a) a_{1} = 0.11 m / s^{2} (b) a_{2} = 0.23 m / s^{2} (c) μ_{k 1} = 0.041 (d) μ_{k 2} = 0.029$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given

New ski is 200 m slope in the Alps, a skier reduced his top-to-bottom time from 61 s with standard skis to 42 s .

Step 2: Understanding the concept

Frictional force is given by the product of coefficient of friction and the normal reaction. Newton’s 2nd law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the object’s mass. Using these concepts, the problem can be solved.

Formula:

$F_{net} = mg sinθ - f_{k}$

Step 3: Calculation for average acceleration with the standard skis

(a)

If the distance is L during time t with initial speed zero and a constant acceleration a, then

$L = a t^{2} / 2,$

Which gives the acceleration for the first (old) pair of skis:

$a_{1} = \frac{2 L}{t_{1}^{2}} = \frac{2 (200 m)}{{(61 s)}^{2}} = 0.11 m / s^{2}$

Step 4: Calculation for average acceleration with the new skis

(b)

The acceleration for the second (new) pair is

$a_{2} = \frac{2 L}{t_{1}^{2}} = \frac{2 (200 m)}{{(42 s)}^{2}} = 0.23 m / s^{2}$

Step 5: Assuming a 3.0° slope, compute the coefficient of kinetic friction for the standard skis

(c)

The net force along the slope acting on the skier of mass m is

$F_{n e t} = m g \sin θ - f_{k} = m g (\sin θ - μ_{k} \cos θ) = m a$

Which we solve for for the first pair of skis:

$μ_{k 1} = \tan θ - \frac{a_{1}}{g \cos θ} = \tan (3 °) - \frac{0.11 m / s^{2}}{(9.8 m / s^{2}) \cos (3 °)} = 0.041$

Step 6: Assuming a 3.0° slope, compute the coefficient of kinetic friction for the new skis

(d)

For second pair, we have

$μ_{k 2} = \tan θ - \frac{a_{2}}{g \cos θ} = \tan (3 °) - \frac{0.23 m / s^{2}}{(9.8 m / s^{2}) \cos (3 °)} = 0.029$

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

Step 2: Understanding the concept

Step 3: Calculation for average acceleration with the standard skis

Step 4: Calculation for average acceleration with the new skis

Step 5: Assuming a 3.0° slope, compute the coefficient of kinetic friction for the standard skis

Step 6: Assuming a 3.0° slope, compute the coefficient of kinetic friction for the new skis

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

Step 2: Understanding the concept

Step 3: Calculation for average acceleration with the standard skis

Step 4: Calculation for average acceleration with the new skis

Step 5: Assuming a 3.0° slope, compute the coefficient of kinetic friction for the standard skis

Step 6: Assuming a 3.0° slope, compute the coefficient of kinetic friction for the new skis

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