# Graphs of Work & Power for Falling Stone

• leftywefty
In summary, the conversation is discussing the task of drawing graphs related to a stone with a mass of 5kg dropping 15m due to gravity. The first graph should show the work done by the stone, and the second graph should show the power of the stone as a function of time. The equations for work and power are also mentioned. The individual is unsure of how to plot the graphs and is seeking clarification on using the power equation involving time or velocity. The conversation also brings up the concept of potential and kinetic energy and how it changes with distance and time.
leftywefty
Draw graphs??

## Homework Statement

A stone of a mass of 5kg drops through a distance of 15m under the influence of gravity. Draw graphs of the work done by the stone and the power of the stone as a function of time. Discuss your results.

## Homework Equations

Work=(force)(displacement)
Power=(work)/(time) or Power=(Force)(velocity)

## The Attempt at a Solution

Ok, so I solved for work
work= (5kg)(9.8m/s^2)(15m)=735J
I don't know what to do now. I would think I need to plot Force on the Y axis, and displacement on the X axis, but I'm not sure.
I'm having the same issue with the second graph
Power=(735J)/(??) The problem says to graph power of the stone as a function of time, so I'm guesing I have to use the power equation that involves time. Can I use Power=(Force)(velocity)? I'm so confused! Help please!

Look at this problem from the point of view of energy. What can you say about the total energy (potential + kinetic) at all times? How does the potential energy change with distance? With time? (how does distance fallen or y position change with time?). Using this can you determine the change in kinetic energy as a function of distance and time?

AM

The graphs for work and power for a falling stone would depend on the assumptions and conditions of the situation. However, we can make some general assumptions and discuss the possible results.

First, let's define the variables in our equations. For work, we have W for work, F for force, and d for displacement. For power, we have P for power, W for work, and t for time.

Now, let's look at the work done by the stone. We can assume that the force acting on the stone is the force of gravity, which is constant at 9.8 m/s^2. This means that the work done by the stone will also be constant, as long as it is falling under the influence of gravity. Therefore, the graph of work vs. displacement will be a straight line, with work being constant at 735J and displacement increasing as the stone falls.

For the power of the stone, we have two equations: P = W/t and P = Fv. Since we know the work done by the stone and the time it takes to fall, we can use the first equation to calculate the power. However, if we want to plot power as a function of time, we can use the second equation since we know the force of gravity and we can calculate the velocity of the stone as it falls. The graph of power vs. time will depend on the velocity of the stone, which will increase as it falls. Therefore, the power graph will start at 0 and gradually increase as the stone falls.

In conclusion, the graphs for work and power of a falling stone will depend on the assumptions and conditions of the situation. However, we can make some general assumptions and discuss the possible results. The graph of work vs. displacement will be a straight line, while the graph of power vs. time will start at 0 and increase as the stone falls.

## 1. What is the relationship between work and power for a falling stone?

The relationship between work and power for a falling stone is that work is the product of force and displacement, while power is the rate at which work is done. As the stone falls, it gains kinetic energy and gains speed, which means it is doing work and increasing its power.

## 2. How does the graph of work and power for a falling stone look like?

The graph of work and power for a falling stone will have a linear shape, with work on the y-axis and time on the x-axis. The slope of the line represents the power, which will increase as the stone falls and gains speed. The area under the curve represents the work done, which will also increase as the stone falls.

## 3. How does the height of the falling stone affect the graph of work and power?

The height of the falling stone affects the graph of work and power by changing the rate at which work is done and power is produced. The higher the stone is dropped from, the greater the initial potential energy and the faster the stone will fall, resulting in a steeper slope on the graph and a larger area under the curve.

## 4. What happens to the graph of work and power if the falling stone encounters air resistance?

If the falling stone encounters air resistance, the graph of work and power will have a less steep slope and a smaller area under the curve. This is because the air resistance will oppose the motion of the stone, reducing its speed and the amount of work and power it produces.

## 5. How can the graph of work and power for a falling stone be used to calculate the velocity of the stone?

The graph of work and power for a falling stone can be used to calculate the velocity of the stone by finding the slope of the line. The slope represents the rate of change of work, which is equal to the force acting on the stone. By using the equation v = at, where v is velocity, a is acceleration (which can be calculated using the force), and t is time, the velocity of the falling stone can be determined.

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