Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Problem 23

A \(1000-\mathrm{N}\) crate rests on a horizontal floor. It is being pulled up by two vertical ropes. The left rope has a tension of \(400 \mathrm{~N}\). Assuming the crate does not leave the floor, what can you say about the tension in the right rope?

Short Answer

Expert verified
Answer: The tension in the right rope is 600 N.

Step by step solution

01

Define the forces acting on the crate

The forces acting on the crate in the vertical direction are: the tension in the left rope (\(T_{left}=400 \mathrm{~N}\)), the tension in the right rope (\(T_{right}\)), and the weight of the crate (\(W=1000 \mathrm{~N}\)). All these forces are acting vertically, either upwards (tension forces) or downwards (weight).
02

Apply Newton's second law of motion

According to Newton's second law of motion, the net force acting on an object is equal to the mass of the object multiplied by its acceleration (\(F_{net} = m \times a\)). In this case, the acceleration of the crate is zero, since it does not leave the floor. Thus, the net force acting on the crate in the vertical direction is also zero. So, we can write the equation for the net force as: \(F_{net} = T_{left} + T_{right} - W = 0\)
03

Solve the equation for the tension in the right rope

We will now solve the equation from Step 2 for the unknown tension in the right rope (\(T_{right}\)): \(T_{left} + T_{right} - W = 0 \) Plugging in the given values for \(T_{left}\) and \(W\), we get: \(400 \mathrm{~N} + T_{right} - 1000 \mathrm{~N} = 0\) Now, we will solve for \(T_{right}\): \(T_{right} = 1000 \mathrm{~N} - 400 \mathrm{~N} = 600 \mathrm{~N}\)
04

State the result

The tension in the right rope is \(600 \mathrm{~N}\). This means that the right rope has higher tension than the left rope, and both ropes combined provide enough upward force to counteract the weight of the crate, ensuring it does not leave the floor.

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

You have a meter stick that balances at the \(50-\mathrm{cm}\) mark. Is it possible for your meter stick to be inhomogeneous?

When only the front wheels of an automobile are on a platform scale, the scale balances at \(8.0 \mathrm{kN} ;\) when only the rear wheels are on the scale, it balances at \(6.0 \mathrm{kN}\). What is the weight of the automobile, and how far is its center of mass behind the front axle? The distance between the axles is \(2.8 \mathrm{~m}\).

A sculptor and his assistant are carrying a wedge-shaped marble slab up a flight of stairs, as shown in the flight of stairs, as shown in the figure. The density of the marble is uniform. Both are lifting straight up as they hold the slab completely stationary for a moment. Does the sculptor have to exert more force than the assistant to keep the slab stationary? Explain.

By considering the torques about your shoulder, estimate the force your deltoid muscles (those on top of the shoulder) must exert on the bone of your upper arm, in order to keep your arm extended straight out at shoulder level. Then, estimate the force the muscles must exert to hold a 10.0 -lb weight at arm's length. You'll need to estimate the distance from your shoulder pivot point to the point where your deltoid muscles connect to the bone of your upper arm in order to determine the necessary forces. Assume the deltoids are the only contributing muscles.

A \(3.0-\mathrm{kg}\) broom is leaning against a coffee table. \(A\) woman lifts the broom handle with her arm fully stretched so that her hand is a distance of \(0.45 \mathrm{~m}\) from her shoulder What torque is produced on her shoulder if her arm is at an angle of \(50^{\circ}\) below the horizontal? a) \(7.0 \mathrm{~N} \mathrm{~m}\) c) \(8.5 \mathrm{~N} \mathrm{~m}\) b) \(5.8 \mathrm{~N} \mathrm{~m}\) d) \(10.1 \mathrm{~N} \mathrm{~m}\)
See all solutions

Recommended explanations on Physics Textbooks

Modern Physics

Read Explanation

Mechanics and Materials

Read Explanation

Measurements

Read Explanation

Atoms and Radioactivity

Read Explanation

Electricity

Read Explanation

Radiation

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