Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Q. 66 (page 157)

A 60kgskater is gliding across frictionless ice at 4.0m/s. Air resistance is not negligible. You can model the skater as a 170−cm-tall,36−cm-diameter cylinder. What is the skater's speed2.0s later?

Short Answer

Expert verified

Speed of the skater after2Sec is3.4m/s.

Step by step solution

01

:Given.

Mass of the skater, m=60kg.

Speed of the skater, v=4m/s.

Diameter of the skater, d=36cm.

Height of the skater,h=170cm.

02

Formula used.

The air friction is given by the formula:

F=12ρ×A×v2

Here,

ρis the density of air.

Ais the surface area of the cylinder.

vis the velocity of the skater.

03

Calculation.

The surface area of the skater is calculated as:A=πdH

Plugging the values in the above equation,

A=π×0.36×1.7=1.92m2.

Now drag force due to air is calculated as:

F=12×1.2×1.92×42=18.43N.

The deceleration on the skater due to air friction is calculated as:

F=ma18.43=60×aa=0.30m/s2.

The speed of the skater after 2sec is calculated as:

role="math" localid="1647774441411" v=u−at=4−0.3×2=3.4m/s.

04

Conclusion.

Speed of the skater after 2sec is3.4m/s.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A horizontal rope is tied to a 50kgbox on frictionless ice. What is the tension in the rope if:

a. The box is at rest?

b. The box moves at a steady5.0m/s?

c. The box has vx=5.0m/s and ax=5.0m/s2 ?

A baggage handler drops your 10kg suitcase onto a conveyor belt running at2.0 m/s. The materials are such that μs=0.50 and . How far is your suitcase dragged before it is riding smoothly on the belt?

FIGURE EX6.10shows the velocity graph of a 2.0kgobject as it moves along the x-axis. What is the net force acting on this object at t=1s? At 4s? At 7s?

A spring-loaded toy gun exerts a variable force on a plastic ball as the spring expands. Consider a horizontal spring and a ball of mass m whose position when barely touching a fully expanded spring is x=0. The ball is pushed to the left, compressing the spring. You’ll learn in Chapter 9that the spring force on the ball, when the ball is at position x(which is negative), can be written as FSppx=-kx, where k is called the spring constant. The minus sign is needed to make the x-component of the force positive. Suppose the ball is initially pushed to x0=-L, then released and shot to the right.

a. Use what you’ve learned in calculus to prove that

ax=vxdvxdx

b. Find an expression, in terms of m, k, and L, for the speed of the ball as it comes off the spring atx=0.

Problems 68 and 69 show a free-body diagram. For each:

a. Write a realistic dynamics problem for which this is the correct free-body diagram. Your problem should ask a question that can be answered with a value of position or velocity (such as "How far?" or "How fast?"), and should give sufficient information to allow a solution.

b. Solve your problem!
See all solutions

Recommended explanations on Physics Textbooks

Translational Dynamics

Read Explanation

Nuclear Physics

Read Explanation

Scientific Method Physics

Read Explanation

Solid State Physics

Read Explanation

Linear Momentum

Read Explanation

Electromagnetism

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free