/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 30 Juggles and Bangles are clowns. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 30

Juggles and Bangles are clowns. Juggles stands on one end of a teeter-totter at rest on the ground. Bangles jumps off a platform 2.5 m above the ground and lands on the other end of the teeter-totter, launching Juggles into the air. Juggles rises to a height of 3.3 m above the ground, at which point he has the same amount of gravitational potential energy as Bangles had before he jumped, assuming both potential energies are measured using the ground as the reference level. Bangles鈥� mass is 86 kg. What is Juggles鈥� mass?

Short Answer

Expert verified
Juggles' mass is approximately 65.15 kg.

Step by step solution

01

Understand the Situation

Juggles and Bangles are using a teeter-totter. When Bangles lands on it, Juggles' potential energy becomes equal to the initial potential energy of Bangles before the jump.
02

List Known Quantities

We know that Bangles' mass \( m_b = 86 \) kg, height before jump \( h_b = 2.5 \) m, and Juggles reaches a height \( h_j = 3.3 \) m. Gravity \( g = 9.8 \) m/s虏.
03

Write the Formula for Potential Energy

The gravitational potential energy \( PE \) is given by \( PE = m \cdot g \cdot h \).
04

Calculate Initial Potential Energy of Bangles

Using Bangles' data, \( PE_b = 86 \times 9.8 \times 2.5 \). Compute this to find the energy.
05

Set Up Equality of Potential Energies

The potential energy of Juggles when he reaches 3.3 meters must equal the initial potential energy of Bangles: \( m_j \cdot g \cdot h_j = 86 \cdot 9.8 \cdot 2.5 \).
06

Solve for Juggles' Mass

Rearrange to find Juggles' mass: \( m_j = \frac{86 \cdot 9.8 \cdot 2.5}{9.8 \times 3.3} \). Simplify the equation and solve.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Gravitational Potential Energy
Gravitational potential energy is the energy that an object possesses due to its position relative to a reference point, often the ground. It's an important concept in physics that helps explain how energy is transferred between objects.

The formula to calculate gravitational potential energy is \( PE = m \cdot g \cdot h \), where:
  • \( m \) is the mass of the object in kilograms,
  • \( g \) is the acceleration due to gravity (approximately 9.8 m/s虏 on Earth),
  • \( h \) is the height of the object above the reference point in meters.
In the exercise, both Juggles and Bangles share the same amount of potential energy at different points. Understanding this formula allows us to set up an equation where the initial energy of Bangles is transferred to Juggles.
Mass Determination
Determining mass using gravitational potential energy is straightforward if you have the potential energy equation. In this exercise, we need to find Juggles' mass after Bangles transfers his energy.

The key here is to recognize that the potential energy Juggles has when he reaches a certain height is equal to the energy Bangles had before jumping.

By setting up the equation \( m_j \cdot g \cdot h_j = m_b \cdot g \cdot h_b \), where \( m_b \) and \( h_b \) are Bangles鈥� mass and height, and \( m_j \) and \( h_j \) are Juggles鈥� mass and height respectively, the values of \( m_j \) can be calculated.
Physics Problem-Solving
Solving physics problems often involves understanding the system, identifying known values, and applying relevant formulas.

In a complex system like the teeter-totter exercise, it is crucial to:
  • List down all known quantities like masses, heights, and gravitational pull,
  • Identify relationships between these quantities,
  • Use appropriate equations, like the potential energy equation.
By following these steps methodically, you break the problem into manageable parts, making it easier to find the solution.
Teeter-Totter Mechanics
The teeter-totter is a classic example used in physics to demonstrate energy transfer and equilibrium.

When Bangles, with a certain mass, jumps onto one end, he generates kinetic energy that transfers to the system, propelling Juggles upwards. The mechanics involve a balance of forces and energy transfer, leading to Juggles reaching a new height.

This principle helps us connect how forces like gravity work in harmony with physical systems to cause movement, especially when mass and height are varied between individuals, as in the clowns鈥� scenario. Understanding these can help demystify the physics behind common playground equipment and complex engineering systems alike.

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 hammer throw is a track-and-field event in which a 7.3-kg ball (the 鈥渉ammer鈥�), starting from rest, is whirled around in a circle several times and released. It then moves upward on the familiar curving path of projectile motion. In one throw, the hammer is given a speed of 29 m/s. For comparison, a .22 caliber bullet has a mass of 2.6 g and, starting from rest, exits the barrel of a gun at a speed of 410 m/s. Determine the work done to launch the motion of (a) the hammer and (b) the bullet.

When an \(81.0-kg\) adult uses a spiral staircase to climb to the second floor of his house, his gravitational potential energy increases by \(2.00 \times 10^{3} J\) . By how much does the potential energy of an \(18.0-kg\) child increase when the child climbs a normal staircase to the second floor?

Bicyclists in the Tour de France do enormous amounts of work during a race. For example, the average power per kilogram generated by seven-time-winner Lance Armstrong (m 75.0 kg) is 6.50 W per kilogram of his body mass. (a) How much work does he do during a 135-km race in which his average speed is 12.0 m/s? (b) Often, the work done is expressed in nutritional Calories rather than in joules. Express the work done in part (a) in terms of nutritional Calories, noting that 1 joule \(=2.389 \times 10^{-4}\) nutritional Calories.

A car accelerates uniformly from rest to 20.0 m/s in 5.6 s along a level stretch of road. Ignoring friction, determine the average power required to accelerate the car if \((a)\) the weight of the car is \(9.0 \times 10^{3} N\) and \((b)\) the weight of the car is \(1.4 \times 10^{4} N .\)

You are moving into an apartment and take the elevator to the 6th floor. Suppose your weight is 685 N and that of your belongings is 915 N. (a) Determine the work done by the elevator in lifting you and your belongings up to the 6th floor (15.2 m) at a constant velocity. (b) How much work does the elevator do on you alone (without belongings) on the downward trip, which is also made at a constant velocity?
See all solutions

Recommended explanations on Physics Textbooks

Translational Dynamics

Read Explanation

Engineering Physics

Read Explanation

Geometrical and Physical Optics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Famous Physicists

Read Explanation

Quantum 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.