September 27

Power
While reading articles, it is important to read critically. There was a magazine article that talked about how the average refrigerator uses less power than a radio clock. The refrigerator used 2kw and it runs for 8 hours a day, the clock radio uses 1 watt for 24 hours. After making the proper calculations, this was proved wrong. The refrigerator uses more power than the clock radio.

P=W/t

W=Pt



Pr=2000w*8*3600

Pr=5.76x10^7J



Pc=1w*24*3600

Pc=86400J






SPRING
A spring with a mass was given an initial velocity and the spring started oscilating. The graphs of the spring oscilating was different for kinetic energy, gravitational energy, and force.
The graph for the force was linear (f=kx), the graphs for kinetic energy and gravitational energy were sinusodial (k=1/2mv^2). The sinusodial graphs had a constant pattern because the velocity was not changing significantly.

Lab
Kinetic Energy and Friction lab was done in class.

Announcements
Write up Kinetic Energy and Friction Lab or Kinetic Energy and Work (Due Friday)
Wednesday review for Midterm
Lab notebooks will be collected on Friday
Cart due on Monday Ocotber 4th

Pre Lab for Friday.

NOTE! The homework for Friday will take you a couple of hours, so please budget your time accordingly!

Recall, you need to turn in the Prediction and Method Questions before class!

PROBLEM #2:

MOTION ON A LEVEL SURFACE

WITH AN ELASTIC CORD

You are helping a friend design a new ride for the State Fair. In this ride, a cart is pulled along a long straight track by a stretched elastic cord like a bungee cord. Before spending money to build it, your friend wants to you to determine if this ride will be safe. Since sudden changes in velocity can lead to whiplash, you decide to find out how the acceleration of the cart changes with time. In particular, you want to know if the greatest acceleration occurs when the sled is moving the fastest or at some other time. To solve this problem, you decide to model the situation in the laboratory with a cart pulled by an elastic cord along a level surface.

How does an object pulled by an elastic cord along a level surface accelerate? Is the acceleration greatest when the velocity is greatest?

Equipment

For this problem you will have a stopwatch, a meter stick, a scissor, a video camera and a computer with a video analysis application .You will also have a cart to roll on a level track. You can attach one end of an elastic cord to the cart and the other end of the elastic cord to an end stop on the track.

Prediction

Make a sketch of how you expect the acceleration-versus-time graph to look for a cart pulled by an elastic cord. Just below that graph make a graph of the velocity versus time on the same time scale. Identify where on your graphs the velocity is largest and the acceleration is largest.

Method Questions

The following questions should help with your prediction and the analysis of your data:

1. Make a sketch of how you expect an acceleration-versus-time graph to look for a cart pulled by an elastic cord. Explain your reasoning. For a comparison, make acceleration-versus-time graphs for a cart moving at constant velocity and a constant acceleration. Write down the equation that best represents each of these accelerations. If there are constants in your equation, what kinematic quantities do they represent? How would you determine these constants from your graphs?

2. Write down the relationship between the acceleration and the velocity of the cart. Use that relationship to construct a velocity-versus-time graph for each case. The connection between the derivative of a function and the slope of its graph will be useful. Write down the equation that best represent each of these velocities. If there are constants in your equation, what kinematic quantities do they represent? How would you determine these constants from your graph? Can any of these constants be determined from the constants in the equation representing the acceleration? Which do you think best represents the velocity of the cart? Change your prediction if necessary.

3. Write down the relationship between the velocity and the position of the cart. Use that relationship to construct a position-versus-time graph for each case. The connection between the derivative of a function and the slope of its graph will be useful. Write down the equation that best represents each of these positions. If there are constants in your equation, what kinematic quantities do they represent? How would you determine these constants from your graph? Can any of these constants be determined from the constants in the equation representing the velocity? Which do you think best represents the position of the cart? Change your prediction if necessary.

Exploration

Test that the track is level by observing the motion of the cart. Attach an elastic cord to the cart and track. Gently move the cart along the track to stretch out the elastic. Be careful not to stretch the elastic too tightly. Start with a small stretch and release the cart. BE SURE TO CATCH THE CART BEFORE IT HITS THE END STOP! Slowly increase the starting stretch until the cart's motion is long enough to get enough data points on the video, but does not cause the cart to come off the track or snap the elastic. Be sure to catch the cart before it collides with the end stop.

Practice releasing the cart smoothly and capturing videos.

Write down your measurement plan.

Make sure everyone in your group gets the chance to operate the camera and the computer.

Measurement

Using the plan you devised in the exploration section, make a video of the cart’s motion. Make sure you get enough points to determine the behavior of the acceleration.

Choose an object in your picture for calibration. Choose your coordinate system.

Why is it important to click on the same point on the car’s image to record its position? Estimate your accuracy in doing so.

Make sure you set the scale for the axes of your graph so that you can see the data points as you take them. Use your measurements of total distance the cart travels and total time to determine the maximum and minimum value for each axis before taking data.

Are any points missing from the position versus time graph? Missing points result from more data being transmitted from the camera than the computer can write to its memory. If too many points are missing, make sure that the size of your video frame is optimal (see Appendix D). It may also be that your background is too busy. Try positioning your apparatus so that the background has fewer visual features.

Analysis

Choose a function to represent the position-versus-time graph. How can you estimate the values of the constants of the function from the graph? You can waste a lot of time if you just try to guess the constants. What kinematic quantities do these constants represent?

Choose a function to represent the velocity-versus-time graph. How can you calculate the values of the constants of this function from the function representing the position-versus-time graph? Check how well this works. You can also estimate the values of the constants from the graph. Just trying to guess the constants can waste a lot of your time. What kinematic quantities do these constants represent?

From the velocity-versus-time graph determine the acceleration of the cart. Use the function representing the velocity-versus-time graph to calculate the acceleration of the cart as a function of time.

Make a graph of the cart’s acceleration as a function of the time. Do you have enough data to convince others of your conclusion?

As you analyze your video, make sure everyone in your group gets the chance to operate the computer.

Conclusion

How does your acceleration-versus-time graph compare with your predicted graph? Are the position-versus-time and the velocity-versus-time graphs consistent with this behavior of acceleration? What is the difference between the motion of the cart in this problem and its motion along an inclined track? What are the similarities? What are the limitations on the accuracy of your measurements and analysis?

What will you tell your friend? Is the acceleration of the cart greatest when the velocity is the greatest? How will a cart pulled by an elastic cord accelerate along a level surface? State your result in the most general terms supported by your analysis.

How would the acceleration-versus-time graph look if you attached another piece of elastic to the other end of the cart and to the opposite end stop of the track? How about the velocity-versus-time and position-versus-time graphs? If you have time, try it.