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If the rate at which work is done on an object is increased, does the power supplied to that object increase, decrease, or stay the same?

Short Answer

Expert verified
The power supplied to the object increases.

Step by step solution

01

Understand the Relationship between Work and Power

Power is defined as the rate at which work is done. Mathematically, power \( P \) is expressed as \( P = \frac{W}{t} \), where \( W \) is the work done and \( t \) is the time taken to do that work.
02

Analyze the Effect of Increased Work Rate

If the rate at which work is done increases, it means that more work is being accomplished in a given amount of time. This translates to an increase in the numerator \( W \) of the power formula, assuming the time \( t \) remains constant or decreases.
03

Determine the Impact on Power

Since power is the quotient of work done and time, an increase in the work done over the same or shorter period results in an increase in power. Thus, the power supplied to the object increases.

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Key Concepts

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

Work-Rate Relationship
In physics, understanding the connection between work and rate is crucial when discussing power. Work refers to the energy transferred when an object is moved over a distance by a force. It's calculated as the product of force and distance: \( W = F \times d \), where \( W \) is the work, \( F \) is the force applied, and \( d \) is the distance moved in the direction of the force. The term 'rate' in this context refers to how quickly this work is being accomplished. When we talk about the work-rate relationship, we're interested in how fast this energy transfer is taking place over time. This is the essence of power. A clear correlation exists: the faster the rate at which work is done, the higher the power. For example, if two cars are pushed over the same distance, but one takes less time, it means the work rate is higher, indicating greater power.
Equation for Power
The equation for power provides a concise way to calculate how much work is done over a specific time frame. It's expressed as:\[ P = \frac{W}{t} \]where \( P \) represents power, \( W \) is the work done, and \( t \) is the time taken. This equation highlights a simple division: the total work is evenly distributed over the time period it takes to perform that work.To understand this equation better, consider a scenario where you need to lift a stack of books onto a shelf. The amount of energy (or work) required is the same whether you take a full minute or just a few seconds to complete the task. However, if you accomplish the task in less time, you are working at a higher rate, resulting in higher power output.This formulation, thus, allows us to quantify power in units of Watts, where one Watt is equal to one joule per second.
Impact of Time on Power
Time, as a factor in the power equation, plays a significant role in determining the power output. The relationship between time and power is inherently inverse. As the time taken to do a given amount of work decreases, the power required increases, assuming the work done stays constant.Consider, for instance, running versus walking up a flight of stairs:- Running up the stairs requires the work to be done in a shorter time, thereby increasing power.- Walking slower takes more time, hence reducing power.When time decreases, the denominator in the power equation \( P = \frac{W}{t} \) becomes smaller, leading to a larger value of power. Conversely, if time increases, the power diminishes, assuming no change in the work done. This fundamental insight underlines the role of time in real-world scenarios like athletic performance and machine efficiency.

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Most popular questions from this chapter

Assess System 1 has a force of \(10 \mathrm{~N}\) and a speed of \(5 \mathrm{~m} / \mathrm{s}\). System 2 has a force of \(20 \mathrm{~N}\) and a speed of \(2 \mathrm{~m} / \mathrm{s}\). Which system has the greater power? Explain.

Predict \& Explain Ball 1 is dropped to the ground from rest. Ball 2 is thrown to the ground with an initial downward speed. Assuming that the balls have the same mass and are released from the same height, is the change in gravitational potential energy of ball 1 greater than, less than, or equal to the change in gravitational potential energy of ball 2? (b) Choose the best explanation from among the following: A. Ball 2 has the greater total energy, and therefore more of its energy can go into gravitational potential energy. b. The gravitational potential energy depends only on the mass of the ball and its initial height above the ground. C. All of the initial energy of ball 1 is gravitational potential energy.

A \(1.3-\mathrm{kg}\) block is pushed up against a stationary spring, compressing it a distance of \(4.2 \mathrm{~cm}\). When the block is released, the spring pushes it away across a frictionless, horizontal surface. What is the speed of the block, given that the spring constant of the spring is \(1400 \mathrm{~N} / \mathrm{m}\) ?

Predict \(\&\) Explain You throw a ball upward and let it fall to the ground. Your friend drops an identical ball straight down to the ground from the same height. (a) Is the change in kinetic energy (from just after the ball is released until just before it hits the ground) of your ball greater than, less than, or equal to the change in kinetic energy of your friend's ball? (b) Choose the best explanation from among the following: C. The change in gravitational potential energy is the same for each ball, which means that the change in kinetic energy must also be the same. A. Your friend's ball converts all of its initial energy into kinetic energy. B. Your ball is in the air longer, which results in a greater change in kinetic energy.

After hitting a long fly ball that goes over the right fielder's head and lands in the outfield, a batter decides to keep going past second base and try for third base. The \(62-\mathrm{kg}\) player begins sliding \(3.4 \mathrm{~m}\) from the base with a speed of \(4.5 \mathrm{~m} / \mathrm{s}\). (a) If the player comes to rest at third base, how much work was done on the player by friction with the ground? (b) What was the coefficient of kinetic friction between the player and the ground?

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