Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 9: Problem 12

A 28 -kg child sits at one end of a 3.5 -m-long seesaw. Where should her \(65-\mathrm{kg}\) father sit so the center of mass will be at the center of the seesaw?

Short Answer

Expert verified
The father should sit 1.5 m away from the center of the seesaw to balance it.

Step by step solution

01

Identify the Given Information

We are given the weight of the child (28 kg), the weight of her father (65 kg) and the length of the seesaw (3.5 m). We assume that the weight of the seesaw is evenly distributed so we can focus on the weights at each end.
02

Set Up the Equation for Balance

Let's say the distance the father should sit from the fulcrum is \(x\). The father's weight will create a torque of \(65g \times x\) in the clockwise direction, where \(g\) is the acceleration due to gravity. The child's weight will create a torque of \(28g \times (3.5 - x)\) in the counter-clockwise direction. To balance the seesaw, these two torques should be equal, i.e., \(65g \times x = 28g \times (3.5 - x)\).
03

Solve for the Unknown

Solve the equation for \(x\). For simplicity, we can divide both sides of the equation by \(g\), getting \(65x = 28(3.5 - x)\). Solving this equation gives \(x = 1.5 m\), meaning the father should sit 1.5 m from the fulcrum. This distance is measured from the center of the seesaw.

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

In a railroad switchyard, a 56 -ton freight car is sent at \(7.0 \mathrm{mi} / \mathrm{h}\) toward a 31 -ton car moving in the same direction at \(2.6 \mathrm{mi} / \mathrm{h} .\) (a) What's the speed of the cars after they couple? (b) What fraction of the initial kinetic energy was lost in the collision?

Roughly where is your center of mass when you're standing?

Two objects of unequal mass, one initially at rest, undergo a onedimensional elastic collision. For a given mass ratio, show that the fraction of the initial energy transferred to the initially stationary object doesn't depend on which object it is.

An object collides elastically with an equal-mass object initially at rest. If the collision isn't head-on, show that the final velocity vectors are perpendicular.

A neutron (mass 1 u) strikes a deuteron (mass 2 u), and they combine to form a tritium nucleus. If the neutron's initial velocity was \(28 \hat{\imath}+17 \hat{\jmath}\) Mm/s and if the tritium leaves the reaction with velocity \(12 \hat{\imath}+20 \hat{\jmath} \mathrm{Mm} / \mathrm{s},\) what was the deuteron's velocity?
See all solutions

Recommended explanations on Physics Textbooks

Classical Mechanics

Read Explanation

Dynamics

Read Explanation

Work Energy and Power

Read Explanation

Torque and Rotational Motion

Read Explanation

Particle Model of Matter

Read Explanation

Waves 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