Graphs of Work & Power for Falling Stone

[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!

 

[Andrew Mason]

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

 

[kerimek]

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.