Optional Practical: Angle of slope

Introduction

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.

Research question

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)
Controlled variables:
All properties of the cart
Nature of the slope
Path of the cart
Length of the slope (L)

Method

  • 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:

  • Make sure you have the right interface - the picture on the screen should look like the one plugged in. If not choose one that does from the "choose datalogger" menu.

  • If using the older interfaces you will need to select the motion sensor by clicking one of the digital channels and selecting from the drop down list.
  • Set the sampling rate to 50 Hz.

  • Drag the graph icon onto the digital input to open a graph of position vs time.

  • Click start and run the cart down the slope, you should see the position increasing as the trolley moves away from the sensor.
  • The acceleration is the gradient of the v vs t graph so you need to change the axis from position to velocity. Do this by clicking the position axis label and choosing velocity. When you have the right graph highlight the part with constant acceleration and find the gradient by choosing linear fit from the best fit options.

Sorry about the Norwegian in the diagrams and screen cast (not sorry if you are Norwegian of course) take it as a bit of International mindedness.

If using LoggerPro:

LoggerPro and the newer PASCO software will automatically recognise that you have plugged in the motion sensor so all you have to do, after connecting the interface is open LoggerPro.

  • Click collect and allow the cart to run down the track.
  • If the interface stops taking measurements after a short time adjust the length of timing to a longer time by clicking the "data collection" button .
  • Measure the acceleration by finding the gradient of the velocity - time graph. This is done by highlighting the relevant section then clicking "linear fit" .

If using a Smart cart and capstone

The Smart cart is a wireless device that connects to the computer via bluetooth so this must be enabled. It probably is already but if you have problems this might be the reason. To switch bluetooth on you go to the settings on a PC or system preferences on a mac.

Switch on the smart cart.

If lights don´t flash you will have to charge it, do this by plugging it into your computer with the USB cable.

Connect to capstone

Start the programme and choose "table and graph"

Click "Hardware setup">bluetooth and choose the smartcart. Make sure you choose the one you are using (it has a number on it).

Selecting data

You are going to measure the velocity and time so choose velocity and time from the dropdown lists in the table headers and graph axis.

Record results by clicking the red record button bottom left.

To plot a best fit line of a portion of the data first click the highlight tool, this opens a box. Move the box over the relevant part of the graph. Now click the curve fitting tool and select linear. This will plot a line for the data in the box.

Theory

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
So a=gh/L

By measuring the acceleration for different slope heights show that a=gh/L and calculate a value for g.

Data collection

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.

Data processing

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.

Data Presentation

  • 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.

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