Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Problem 13

A child of mass \(40.0 \mathrm{kg}\) is sitting on a horizontal seesaw at a distance of \(2.0 \mathrm{m}\) from the supporting axis. What is the magnitude of the torque about the axis due to the weight of the child?

Short Answer

Expert verified
Answer: The magnitude of the torque about the supporting axis due to the weight of the child is 784.8 N·m.

Step by step solution

01

Calculate the weight of the child

To calculate the weight of the child, we will use the formula for weight, which is given by \(W = mg\), where \(m\) is the mass of the child, and \(g\) is the acceleration due to gravity (approximately \(9.81 \mathrm{m/s^2}\)). So, for the child with a mass of \(40.0 \mathrm{kg}\), the weight will be: \(W = (40.0 \mathrm{kg})(9.81 \mathrm{m/s^2}) = 392.4 \mathrm{N}\).
02

Calculate the torque

Now that we have the weight of the child, we can calculate the torque using the formula \(\tau = rF\sin\theta\). In this case, the distance from the supporting axis is \(r = 2.0 \mathrm{m}\), the force is the weight of the child \(F = 392.4 \mathrm{N}\), and the angle between the force and the distance is \(\theta = 90^\circ\). So, the torque will be: \(\tau = (2.0 \mathrm{m})(392.4 \mathrm{N})\sin(90^\circ) = (2.0 \mathrm{m})(392.4 \mathrm{N})(1) = 784.8 \mathrm{N \cdot m}\). Thus, the magnitude of the torque about the supporting axis due to the weight of the child is \(784.8 \mathrm{N \cdot m}\).

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 house painter is standing on a uniform, horizontal platform that is held in equilibrium by two cables attached to supports on the roof. The painter has a mass of \(75 \mathrm{kg}\) and the mass of the platform is \(20.0 \mathrm{kg} .\) The distance from the left end of the platform to where the painter is standing is \(d=2.0 \mathrm{m}\) and the total length of the platform is $5.0 \mathrm{m}$ (a) How large is the force exerted by the left-hand cable on the platform? (b) How large is the force exerted by the right-hand cable?
A 2.0 -kg uniform flat disk is thrown into the air with a linear speed of \(10.0 \mathrm{m} / \mathrm{s} .\) As it travels, the disk spins at 3.0 rev/s. If the radius of the disk is \(10.0 \mathrm{cm},\) what is the magnitude of its angular momentum?
The pull cord of a lawnmower engine is wound around a drum of radius $6.00 \mathrm{cm} .\( While the cord is pulled with a force of \)75 \mathrm{N}$ to start the engine, what magnitude torque does the cord apply to the drum?
A person is doing leg lifts with 3.0 -kg ankle weights. She is sitting in a chair with her legs bent at a right angle initially. The quadriceps muscles are attached to the patella via a tendon; the patella is connected to the tibia by the patella tendon, which attaches to bone \(10.0 \mathrm{cm}\) below the knee joint. Assume that the tendon pulls at an angle of \(20.0^{\circ}\) with respect to the lower leg, regardless of the position of the lower leg. The lower leg has a mass of \(5.0 \mathrm{kg}\) and its center of gravity is $22 \mathrm{cm}\( below the knee. The ankle weight is \)41 \mathrm{cm}$ from the knee. If the person lifts one leg, find the force exerted by the patella tendon to hold the leg at an angle of (a) \(30.0^{\circ}\) and (b) \(90.0^{\circ}\) with respect to the vertical.
A sign is supported by a uniform horizontal boom of length \(3.00 \mathrm{m}\) and weight \(80.0 \mathrm{N} .\) A cable, inclined at an angle of \(35^{\circ}\) with the boom, is attached at a distance of \(2.38 \mathrm{m}\) from the hinge at the wall. The weight of the sign is \(120.0 \mathrm{N} .\) What is the tension in the cable and what are the horizontal and vertical forces \(F_{x}\) and \(F_{y}\) exerted on the boom by the hinge? Comment on the magnitude of \(F_{y}\).
See all solutions

Recommended explanations on Physics Textbooks

Oscillations

Read Explanation

Dynamics

Read Explanation

Space Physics

Read Explanation

Kinematics Physics

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Mechanics and Materials

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