# Optional Practical: Rolling ball

### Introduction

In this practical the motion of a ball rolling off the end of a ramp will be analysed using video. The video can either be taken with a camera or phone or using the webcam on the computer. To record using the webcam you need to open LoggerPro and insert > video capture. If using a camera save the movie onto the desktop, open LoggerPro and insert > movie. The format can be mov, mpeg, avi or wav but mov might be the best choice as this definitely works.

#### Research Question

What is the relationship between the velocity of a ball after rolling down a slope and the height of the slope?

**Independent variable**: Height of slope (h)**Dependent variable:**Final velocity of ball (v)**Controlled variables:**

Angle of slope

Size and mass of ball

Nature of surface of slope

Nature of surface after slope

### Theory

When a ball rolls down a slope it accelerates with a constant acceleration of gsinϑ (ignoring friction and air resistance).

If acceleration is constant then v^{2} = u^{2} + 2as

But if the initial velocity = 0 then v^{2} = 2as

But a = gsinϑ where sinϑ = h/s

So v ^{2}= 2gsh/s = 2gh

### Method

The velocity of the ball is going to be measured by analysing a video. This can be done using your webcam or a camera.

- Position the camera so that it records the motion of the ball after the slope (this region must be flat so that the velocity of the ball changes as little as possible).
- Make 6 marks on the slope at different heights with some tape. These will be the starting points. Measure the height h of each point.
- Make two marks a distance of 50cm apart on the flat surface (table) with tape. These will be used to calibrate the video so must be in the picture.
- Place the ball on the marker, start the camera and release the ball.
- Without stopping the camera record the motion of the ball for each height.
- Save the video on your desktop.

### Analysing the video

To analyze the movie follow the steps shown in the screen cast below.

By analysing the video you are going to use a graphical method to show that v^{2} = 2gh and find a value for g.

### Data Collection

Make a table in excel like the one below and add your height up the ramp and the velocities that you have found by analyzing the video. In your report you should also include a copy of the video analysis graphs.

Estimate the uncertainty in h by considering how well you can use the ruler.

Estimate the uncertainty in v by trying several different best fit lines for one of the velocities. You could also try repeating one of the measurements 5 times to see how much it varies. The uncertainty is then (max-min)/2. Write down the reasons for your decisions under the table.

### Data Processing

Since v^{2} = 2gh a graph of v^{2} vs h should be linear. Before plotting this you will need to calculate v^{2} and the uncertainty in v^{2}^{ }. This should be done in a spreadsheet like the one below.

Where v_{max}^{2} = (v+ uncertainty)^{2} and v_{min}^{2} = (v- uncertainty)^{2}

and uncertainty in v^{2} = (v_{max}^{2} - v_{min}^{2} )/2

When you have calculated the uncertainty column reduce the significant figures to 1 then adjust v^{2 }so that it has the same number of decimal places as the uncertainty

### Data presentation

- You are going to plot v
^{2}vs h in Logger pro so copy and paste these columns into the logger pro table. You will also need the unc. in v^{2}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 v^{2}. - 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

Calculate a value for g from the gradient of your line. Also calculate the maximum and minimum values from the steepest and least steep lines and find the uncertainty from (max-min)/2. Compare your value with the accepted.

Your value is probably too small, why might this be. Use evidence from your graph

- Was the relationship linear?
- Did the error bars reflect the spread of data?
- Were there big random errors?
- Is the intercept (0,0)? If not could this have been caused by a systematic error?

If you did this experiment carefully you shouldn’t have got big random errors so you can’t blame a poor result on bad technique or faulty instruments. Perhaps the assumptions made when deriving v^{2} = 2gh were incorrect.

- Did all of the PE get converted into translational KE?
- Does the fact that the ball is rolling affect the result?
- Did air resistance or friction cause any problems?

When you have identified the problem try to suggest ways that you could perform the experiment that would lead to a value of g closer to expected.