Work and Energy: predicted/measured from Force graph

In summary, the conversation discusses a DataStudio run with a cart and rubber band, and the use of graphs to analyze motion. The mass of the cart is given and the final speed is predicted using work done by the rubber band. The percent difference between the predicted and measured final speed is also calculated. However, the standard deviation for the predicted speed cannot be computed with only one trial.
  • #1
toboldlygo
32
2

Homework Statement


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.

var_force_run2.PNG


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

Homework Equations



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

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.
 
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  • #2
The standard deviation cannot be computed for only one trial. Read the question more carefully.
 
  • #3
Dr. Courtney said:
The standard deviation cannot be computed for only one trial. Read the question more carefully.

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?
 

FAQ: Work and Energy: predicted/measured from Force graph

What is work and energy?

Work and energy are two closely related concepts in physics. Work is defined as the amount of force applied to an object multiplied by the distance it moves in the direction of the force. Energy, on the other hand, is the ability of an object to do work or cause a change in its surroundings.

How is work and energy related to force?

Force is the external influence that can cause a change in the energy or motion of an object. When a force is applied to an object and it moves in the direction of the force, work is being done and energy is being transferred to the object.

What is the predicted/measured relationship between force and work?

According to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy. This means that the amount of work done on an object is directly proportional to the force applied to it and the distance it moves in the direction of the force.

How can we represent the relationship between force and work?

The relationship between force and work can be represented graphically using a force vs. distance graph. The area under the graph represents the work done on the object, with the force on the y-axis and the distance on the x-axis.

How can we use a force graph to measure energy?

A force graph can be used to measure energy by calculating the area under the graph, which represents the work done on the object. This can then be used to determine the amount of energy transferred to the object.

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