Optional Practical: Angle of slope
In this practical the acceleration of a cart down a slope will be measured for different slope angles. By plotting a graph of the results a value for the acceleration due to gravity will be determined.
What is the relationship between the height of a slope and the acceleration of a cart rolling down it?
Independent variable: The height of the slope (h)
Dependent variable: The acceleration of the cart (a)
All properties of the cart
Nature of the slope
Path of the cart
Length of the slope (L)
- Set the motion sensor up on the end of the inclined track as in the photo.
- Plug the motion sensor into one of the digital inputs of the interface
- Plug the interface into the power supply and connect it to the computer via the USB port.
If using data studio:
If using LoggerPro:
If using a Smart cart and capstone
When a cart travels down a slope its acceleration is equal to the component of g down the slope (ignoring friction and air resistance).
a = gsinϑ
where sinϑ = h/L
By measuring the acceleration for different slope heights show that a=gh/L and calculate a value for g.
The raw data is in the form of a v-t graph so include a screen shot of one of these in you report. Measure the acceleration for a range of h values and enter them into a table like the one below. If you have time repeat each measurement 4 times.
Estimate how well you can determine the uncertainty in h.
Estimate the uncertainty in a by thinking how well you can judge the gradient of the best fit line. The spread of data will give a better idea of the uncertainty and it is this that you will use on the graph. Write the justification of uncertainties under your table.
The processing in this experiment is quite simple. Just find the average value for a and its uncertainty from the spread of data (max-min)/2. Your spread sheet should be like the one below:
Reduce the significant figures of the uncertainty to 1 and then the decimal places of Av. a to the same number as the uncertainty.
- You are going to plot a vs h in Logger pro so copy and paste these columns into the LoggerPro table. You will also need the unc. in a so create another column (Data – new manual column) and paste that too.
- Add relevant headers and units by double clicking the header and filling in the details.
- Display error bars on the points by double clicking the header and choosing the options tab. The error in h is fixed but you will use your 3rd column for a.
- Place steepest and least steep lines using the manual option under curve fit.
- Calculate the gradients of the lines and quote them under the graph.
Conclusion and Evaluation
- a = gh/L so the gradient of the line = g/l Calculate g from the gradient of the best fit line.
- Calculate the uncertainty in g from the steepest and least steep lines
- Compare your value of g to the accepted value.
Use you graph to deduce which measurement had the biggest uncertainty
- Do the error bars reflect the actual spread of data?
- Is the intercept (0,0)?
- Was the relationship linear?
- Does there appear to be a non linear trend.
Try to explain any irregularities in the graph by considering the method, you can also look at the raw data table for more evidence.
- Did air resistance or friction cause any problems?
- Were there any problems with the apparatus?
- Were the controlled variables kept constant?
Suggest ways that the set up could be improved to address the weaknesses suggested in the evaluation.