/*! 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 42 An assistant for the football te... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 42

An assistant for the football team carries a \(30-\mathrm{kg}\) cooler of water from the top row of the stadium, which is \(20 \mathrm{~m}\) above the field level, down to the bench area on the field. (a) If the speed of the cooler is constant throughout the trip, calculate the work done by the assistant. (b) How much work is done by the force of gravity on the cooler of water?

Short Answer

Expert verified
The work done by the assistant is \(5880\, \mathrm{J}\), and the work done by the force of gravity is also \(5880\, \mathrm{J}\) but in the opposite direction.

Step by step solution

01

Calculate the work done by the assistant

Given the weight of the cooler is \(30 \mathrm{kg}\) and the height it is being carried through is \(20 \mathrm{m}\), the assistant is working against gravity to carry the cooler. As the cooler's speed is constant, the work done by the assistant is the same as the work done by gravity but in opposite direction. Thus, the assistant must exert a force equal to the weight of the cooler to prevent it from accelerating downwards. The weight can be calculated using the formula: Weight = mass \(\times\) gravity Where g (gravity) is approximately \(9.8 \mathrm{m/s}^{2}\). Therefore the work done by the assistant, W, can be given by the formula: W = force \(\times\) distance Force here is the weight of the cooler (mass \(\times\) gravity), and the distance is \(20 \mathrm{m}\).
02

Calculate the work done by gravity

The work done by gravity can be calculated by the same formula as in step 1, i.e. work W = force \(\times\) distance. The force acting on the cooler is the force caused by gravity, which is equal to the weight of the cooler (mass \(\times\) gravity), and the distance is the same \(20 \mathrm{m}\). The direction of the force of gravity is the same as the displacement, so no negative sign is needed in this case.

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.

Work Done by Gravity
When we talk about the work done by gravity, we are considering how gravity affects an object as it moves a certain distance. In physics, work is defined as the product of force and displacement in the direction of the force. Gravity, being a constant force acting downwards, is calculated using the formula:
\[\text{Weight} = \text{mass} \times \text{gravity}\]Here, gravity is approximately 9.8 m/s虏. So, for our cooler weighing 30 kg:
  • Weight = 30 kg \( \times \) 9.8 m/s虏 = 294 N
The work done by gravity is then:
\[W = \text{force} \times \text{distance} = 294 \text{ N} \times 20 \text{ m} = 5880 \text{ J}\]Gravity does positive work because the cooler moves in the direction of the gravitational force. This means gravity helps in moving the cooler downwards, using its weight and the displacement.
Constant Speed
Maintaining a constant speed while moving an object means that the net force acting on the object is zero. In our scenario, the assistant is carrying the cooler down 20 meters without changing its speed. It鈥檚 crucial because:
  • The force applied by the assistant must equal the opposing force of gravity.
  • This balance prevents acceleration, ensuring constant speed.
When forces are balanced:
- No additional force is required to change the speed. - Energy is spent to counteract gravity without altering motion speed.
This ultimately means that the overall energy expenditure by the assistant is equal to the work required to just hold the cooler from accelerating due to gravity.
Force and Distance
In physics, understanding the relationship between force and distance is crucial when calculating work. Work is done when a force causes an object to move over a distance. The key points include:
  • Force applied is responsible for the change or prevention of motion.
  • Distance over which the force acts is a critical factor in work done.
For the cooler:
- Force needed to hold the cooler is its weight (mass \( \times \) gravity).- Distance is the vertical displacement (20 m in this case).
The combination of force and distance gives us the work done using the formula:
\[W = \text{force} \times \text{distance}\]So, understanding both parameters perfectly informs us how energy is transferred or altered within the system, especially in scenarios involving gravity.

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 bicyclist maintains a constant speed of \(4 \mathrm{~m} / \mathrm{s}\) up a hill that is inclined at \(10^{\circ}\) with the horizontal. Calculate the work done by the person and the work done by gravity if the bicycle moves a distance of \(20 \mathrm{~m}\) up the hill. The combined mass of the rider and the bike is \(90 \mathrm{~kg}\).

Sports A man on his luge (total mass of \(88 \mathrm{~kg}\) ) emerges onto the horizontal straight track at the botrom of the hill with an initial speed of \(28 \mathrm{~m} / \mathrm{s}\). If the luge and rider slow at a constant rate of \(2.8 \mathrm{~m} / \mathrm{s}^{2}\), what work is done on them by the force that slows them?

Biology An adult dolphin is about \(5 \mathrm{~m}\) long and weighs about \(1600 \mathrm{~N}\). How fast must he be moving as he leaves the water in order to jump to a height of \(2.5 \mathrm{~m}\) ? Ignore any effects due to air resistance.

Calc The force that acts on an object is given by \(\vec{F}=3 x \hat{i}+4 y \hat{j}\). (The multiplicative constants carry SI units.) Calculate the work done on the object by the force when the object moves from the origin \((0,0)\) to the point \((3,4)\). SSM

Adam and Bobby are twins who have the same weight. Adam drops to the ground from a tree at the same time that Bobby begins his descent down a frictionless slide. If they both scart at the same height above the ground, how do their kinetic energies compare when they hit the ground? A. Adam has greater kinetic energy than Bobby. B. Bobby has greater kinetic energy than Adam. C. They have the same kinetic energy. D. Bobby has twice the kinetic energy as Adam. E. More information is required to compare their kinetic energies. SSM
See all solutions

Recommended explanations on Physics Textbooks

Waves Physics

Read Explanation

Famous Physicists

Read Explanation

Engineering Physics

Read Explanation

Radiation

Read Explanation

Fundamentals of Physics

Read Explanation

Magnetism

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.