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Chapter 7: Problem 4

A farmhand pushes a \(26-k g\) bale of hay 3.9 m across the floor of a barn. If she exerts a horizontal force of \(88 \mathrm{N}\) on the hay, how much work has she done?

Short Answer

Expert verified
The work done is 343.2 J.

Step by step solution

01

Understanding the Concept of Work

In physics, work is defined as the amount of energy transferred by a force acting through a distance. The formula to calculate work is given by \( W = F \cdot d \cdot \cos(\theta) \), where \(W\) is the work done, \(F\) is the force applied, \(d\) is the displacement, and \(\theta\) is the angle between the force and the displacement direction. In this case, the force is applied horizontally, meaning \(\theta = 0\), so \(\cos(\theta) = 1\).
02

Substituting Values into the Work Formula

We are given that the force \(F = 88\, \text{N}\) and the displacement \(d = 3.9\, \text{m}\). Since \(\theta = 0\), the angle between the force and displacement is zero. Substitute these values into the work formula: \( W = 88 \times 3.9 \times \cos(0) = 88 \times 3.9 \times 1 \).
03

Calculating the Work Done

Perform the multiplication to find the work done. Calculate \( 88 \times 3.9 \), which equals \(343.2\, \text{J}\). Therefore, the work done in pushing the bale of hay is \(343.2\, \text{J}\).

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Key Concepts

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

Energy Transfer
Energy transfer occurs when a force moves an object over a distance. In this scenario, the energy is transferred from the farmhand to the bale of hay. This transfer energizes the bale and moves it across the barn.
Consider these basic ideas:
  • In physics, work is essentially another term for energy transfer through movement.
  • When you push an object with a force and make it move, you're transferring energy from yourself to the object.
  • This transferred energy then becomes part of the total mechanical energy of the object.
In our example, the initial energy comes from the farmhand exerting force. This energy transfer allows the hay to change its position by displacing it across the barn.
Force Application
The application of force is crucial for moving an object. In this exercise, the farmhand uses a force of 88 Newtons to push the bale of hay. Understanding this can help you comprehend how much force is needed to move different objects.
Some key points to remember about force application are:
  • Force is a vector quantity, which means it has both magnitude and direction.
  • In this instance, the force is applied horizontally, which perfectly aligns with the direction of the intended movement.
  • A greater force would result in greater acceleration of the hay, assuming the mass stays the same.
Hence, the magnitude and direction of the force determine the movement and final destination of the object.
Displacement
Displacement refers to how much the position of an object changes and in what direction. Here, the bale of hay moves 3.9 meters across the barn, representing its displacement.
To get a clearer understanding, keep in mind:
  • Displacement is also a vector quantity, meaning it has both length and direction.
  • It's different from distance, which considers the entire path traveled, while displacement measures the shortest route between two points.
  • If the farmhand had pushed the bale in a curvy path, the displacement would still be calculated as the straight-line distance from start to end.
Thus, displacement is a critical component in calculating work, as it directly influences how much energy is needed to move an object from one point to another.

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Most popular questions from this chapter

A small plane tows a glider at constant speed and altitude. If the plane does \(2.00 \times 10^{5} \mathrm{J}\) of work to tow the glider \(145 \mathrm{m}\) and the tension in the tow rope is \(2560 \mathrm{N}\), what is the angle between the tow rope and the horizontal?

A 65-kg bicyclist rides his 8.8-kg bicycle with a speed of \(14 \mathrm{m} / \mathrm{s} .\) (a) How much work must be done by the brakes to bring the bike and rider to a stop? (b) How far does the bicycle travel if it takes \(4.0 \mathrm{s}\) to come to rest? \((\mathrm{c})\) What is the magnitude of the braking force?

CE Car 1 has four times the mass of car 2, but they both have the same kinetic energy. If the speed of car 2 is \(v\), is the speed of car 1 equal to \(v / 4, v / 2,2 v,\) or \(4 v ?\) Explain.

IP A \(1300-\mathrm{kg}\) car delivers a constant 49 hp to the drive wheels. We assume the car is traveling on a level road and that all frictional forces may be ignored. (a) What is the acceleration of this car when its speed is \(14 \mathrm{m} / \mathrm{s} ?\) (b) If the speed of the car is doubled, does its acceleration increase, decrease, or stay the same? Explain. (c) Calculate the car's acceleration when its speed is \(28 \mathrm{m} / \mathrm{s}\).

IP A kayaker paddles with a power output of \(50.0 \mathrm{W}\) to maintain a steady speed of \(1.50 \mathrm{m} / \mathrm{s}\). (a) Calculate the resistive force exerted by the water on the kayak. (b) If the kayaker doubles her power output, and the resistive force due to the water remains the same, by what factor does the kayaker's speed change?
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