Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Problem 7

11.7 A \(15-\mathrm{kg}\) child sits on a playground seesaw, \(2.0 \mathrm{~m}\) from the pivot. A second child located \(1.0 \mathrm{~m}\) on the other side of the pivot would have to have a mass of _________ to lift the first child off the ground. a) greater than \(30 \mathrm{~kg} \quad\) c) equal to \(30 \mathrm{~kg}\) b) less than \(30 \mathrm{~kg}\)

Short Answer

Expert verified
Answer: The mass of the second child required to lift the first child off the ground is 30 kg.

Step by step solution

01

Identifying the given variables

The given variables in this problem are: 1. Mass of first child = \(15~kg\) 2. Distance of the first child from the pivot = \(2.0~m\) 3. Distance of the second child from the pivot = \(1.0~m\) Our goal is to find the mass of the second child so that the first child is lifted off the ground.
02

Balancing the Torque

In order to balance the torque, we follow the equation: \(τ_1 = τ_2\) where \(τ_1\) is the torque created by the first child and \(τ_2\) is the torque created by the second child. Torque can be calculated as: \(τ = (force) * (distance~to~pivot)\) Force is the product of mass and gravitational acceleration, \(F = mg\). Therefore, \(τ = (mg) * (distance~to~pivot)\)
03

Applying the Torque equation

Now, we need to balance the torque created by both children: \((m_1g)d_1 = (m_2g)d_2\) Where \(m_1 = 15~kg\), \(d_1 = 2.0~m\), \(d_2 = 1.0~m\) and we need to find \(m_2\). Gravitational acceleration \(g\) will be the same for both children and cancels out when equating torques. \((15~kg)(2.0~m) = (m_2)(1.0~m)\)
04

Solve for the mass of the second child

To find the mass of the second child, we can rearrange the equation: \(m_2 = \frac{(15~kg)(2.0~m)}{1.0~m}\) \(m_2 = 30~kg\) The mass of the second child required to lift the first child off the ground is equal to \(30~kg\). So, the correct answer is c) equal to \(30~kg\).

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 construction supervisor of mass \(M=92.1 \mathrm{~kg}\) is standing on a board of mass \(m=27.5 \mathrm{~kg} .\) Two sawhorses at a distance \(\ell=3.70 \mathrm{~m}\) apart support the board. If the man stands a distance \(x_{1}=1.07 \mathrm{~m}\) away from the left-hand sawhorse as shown in the figure, what is the force that the board exerts on that sawhorse?

If the wind is blowing strongly from the east, stable equilibrium for an open umbrella is achieved if its shaft points west. Why is it relatively easy to hold the umbrella directly into the wind (in this case, easterly) but very difficult to hold it perpendicular to the wind?

A track has a height that is a function of horizontal position \(x\), given by \(h(x)=x^{3}+3 x^{2}-24 x+16\). Find all the positions on the track where a marble will remain where it is placed. What kind of equilibrium exists at each of these positions?

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) \(10.1 \mathrm{~N} \mathrm{~m}\)

A trapdoor on a stage has a mass of \(19.2 \mathrm{~kg}\) and a width of \(1.50 \mathrm{~m}\) (hinge side to handle side). The door can be treated as having uniform thickness and density. A small handle on the door is \(1.41 \mathrm{~m}\) away from the hinge side. \(\mathrm{A}\) rope is tied to the handle and used to raise the door. At one instant, the rope is horizontal, and the trapdoor has been partly opened so that the handle is \(1.13 \mathrm{~m}\) above the floor. What is the tension, \(T,\) in the rope at this time?
See all solutions

Recommended explanations on Physics Textbooks

Medical Physics

Read Explanation

Fields in Physics

Read Explanation

Rotational Dynamics

Read Explanation

Measurements

Read Explanation

Translational Dynamics

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