# Homework Help: Work and Energy: predicted/measured from Force graph

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1. Nov 8, 2015

### toboldlygo

1. The problem statement, all variables and given/known data
A screen grab of a DataStudio run with a cart being pulled by a rubber band connected to a force sensor attached to the end of the track is shown below. The two graphs have the same horizontal axis: position of the cart from the motion sensor. The vertical axis on one graph is velocity of the cart and on the other it is force measured by the force sensor. The DataStudio tools have been used to mark two points on the horizontal, and the area between the force data and the axis is shown in gray.

The mass of the cart is 1.229 kg. The rest of the data can be obtained from the graph above. All answers below must be correct to 3 significant figures.

What is the final speed of the cart predicted by the work done by the rubber band, assuming that friction is negligible.

Find the percent difference between between the predicted and measured final speed, expressed as a percent of the measured speed.

Assume that the standard deviation in a collection of similar measurements to the one shown in the figure were σW = 0.114 J for the work W done by the rubber band. Given this uncertainty, calculate the uncertainty for the predicted speed

2. Relevant equations

ΔK=ΔW
ΔK= .5Mv2
σv= εvpred * vpred where ε is the fractional standard deviation.

3. The attempt at a solution

I'm not really sure what to do in this situation. I found the predicted v value by taking the work and setting it equal to the kinetic energy, and then I found the measured v by squinting and zooming into the graph and guessing final velocity. I used those two to get a percent difference, but I don't know how to get the standard deviation. I also don't know if I did the first two parts correctly. Thanks in advance for any help.

2. Nov 8, 2015

### Dr. Courtney

The standard deviation cannot be computed for only one trial. Read the question more carefully.

3. Nov 8, 2015

### toboldlygo

They're asking for the uncertainty of the predicted velocity, and using σ to depict that. Doesn't σ and uncertainty denote the standard deviation?