# 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:

#### If using LoggerPro:

### If using a Smart cart and capstone

### 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 3
^{rd}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.