Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Problem 60

A crate of potatoes of mass \(18.0 \mathrm{kg}\) is on a ramp with angle of incline \(30^{\circ}\) to the horizontal. The coefficients of friction are \(\mu_{\mathrm{s}}=0.75\) and \(\mu_{\mathrm{k}}=0.40 .\) Find the frictional force (magnitude and direction) on the crate if the crate is sliding up the ramp.

Short Answer

Expert verified
Answer: The magnitude of the frictional force on the crate is 61.12 N, and the direction is downwards along the ramp.

Step by step solution

01

Calculate gravitational force

First, we need to find the gravitational force acting on the crate. The gravitational force (weight) can be calculated using the formula: \(F_g = m \times g\) where \(F_g\) is the gravitational force, \(m\) is the mass of the crate, and \(g\) is the acceleration due to gravity (approximately \(9.81 \, m/s^2\)). Given mass \(m = 18.0 \, kg\), we have: \(F_g = 18.0 \, kg \times 9.81 \, m/s^2 = 176.58 \, N\)
02

Calculate normal force

Now that we have the gravitational force on the crate, we can calculate the normal force acting on the crate. The normal force is perpendicular to the ramp surface and can be calculated using the formula: \(F_n = F_g \times \cos{\theta}\) where \(F_n\) is the normal force and \(\theta\) is the angle of inclination. Given angle \(\theta = 30^{\circ}\), we have: \(F_n = 176.58 \, N \times \cos{30^{\circ}} = 152.81 \, N\)
03

Calculate frictional force

To find the frictional force acting on the crate when it is sliding up the ramp, we can use the formula for kinetic friction: \(F_f = \mu_k \times F_n\) where \(F_f\) is the frictional force and \(\mu_k\) is the coefficient of kinetic friction. Given coefficient of kinetic friction \(\mu_k = 0.40\), we have: \(F_f = 0.40 \times 152.81 \, N = 61.12 \, N\) Since the crate is sliding up the ramp, the frictional force acts in the opposite direction, i.e., down the ramp. Therefore, the magnitude of the frictional force on the crate is \(61.12 \, N\), and the direction is downwards along the ramp.

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

The mass of the Moon is 0.0123 times that of the Earth. A spaceship is traveling along a line connecting the centers of the Earth and the Moon. At what distance from the Earth does the spaceship find the gravitational pull of the Earth equal in magnitude to that of the Moon? Express your answer as a percentage of the distance between the centers of the two bodies.
Refer to Example 4.19. What is the apparent weight of the same passenger (weighing \(598 \mathrm{N}\) ) in the following situations? In each case, the magnitude of the elevator's acceleration is $0.50 \mathrm{m} / \mathrm{s}^{2} .$ (a) After having stopped at the 15 th floor, the passenger pushes the 8 th floor button; the elevator is beginning to move downward. (b) The elevator is moving downward and is slowing down as it nears the 8 th floor.
A woman who weighs \(600 \mathrm{N}\) sits on a chair with her feet on the floor and her arms resting on the chair's armrests. The chair weighs $100 \mathrm{N}\(. Each armrest exerts an upward force of \)25 \mathrm{N}$ on her arms. The seat of the chair exerts an upward force of \(500 \mathrm{N}\). (a) What force does the floor exert on her feet? (b) What force does the floor exert on the chair? (c) Consider the woman and the chair to be a single system. Draw an FBD for this system that includes all of the external forces acting on it.
An \(85-\mathrm{kg}\) skier is sliding down a ski slope at a constant velocity. The slope makes an angle of \(11^{\circ}\) above the horizontal direction. (a) Ignoring any air resistance, what is the force of kinetic friction acting on the skier? (b) What is the coefficient of kinetic friction between the skis and the snow?
A parked automobile slips out of gear, rolls unattended down a slight incline, and then along a level road until it hits a stone wall. Draw an FBD to show the forces acting on the car while it is in contact with the wall.
See all solutions

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Read Explanation

Electromagnetism

Read Explanation

Particle Model of Matter

Read Explanation

Oscillations

Read Explanation

Force

Read Explanation

Nuclear Physics

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