# Momentum graph + why graph should be curved line

1. Oct 3, 2015

### Barclay

1. The problem statement, all variables and given/known data
A student investigates the motion of a trolley as it rolls down a ramp .... a data logger records the time the beam was broken for and uses this to calculate the speed of the trolley.

Experiment results are:
Height of ramp (cm) / Momentum of trolley at the bottom
15 / 1.1
20 / 1.3
25 / 1.5
30 / 1.6
35 / 1.8
40 / 2.0

Q1. Draw a graph of the results with height on x-axis and momentum on y-axis

Q2. Describe the pattern of the graph.

Q3. Do the data points on the graph suggest that the line should go through the origin?

Q4. Using ideas about momentum, explain whether you would expect the line to go through the origin.

2. Relevant equations

momentum = mass x velocity

3. The attempt at a solution

Q1 - done that

Q2. It looks like a straight line .... well more or less (allowing for experimental error). I say as the height of the ramp increases the momentum increases.

The book answer also says "as the height of the ramp increases the momentum increases" but then says "It is not proportional". I do not understand that. A straight line, I thought means proportionality

Q3. Y-axis is cut at 0.6 kg m/s .... this is correct according to the book

Q4.
I say YES the line should pass through the origin because at the beginning velocity is ZERO so momentum is ZERO from momentum = mass x velocity but the line cuts the y-axis at 0.6 kg m/s.

The book says the student should make more measurements between 0 cm and 15 cm but friction slows the trolley down preventing this.

My main confusion is why the graph looks like a straight line but the book suggests it should be curved and pass to ZERO

2. Oct 3, 2015

### blurryface

I think the book is saying that the height of the ramp and the momentum of the trolley are directly related but not perfectly proportional: meaning that the height of the ramp increasing also increases the momentum of the trolley, but they do not increase in proportional manner (1/1 ratio)

3. Oct 4, 2015

### Barclay

But why not? The graph looks more or less like a straight line so should mean proportionality - as the height of the ramp increases the trolley should travel proportionately faster and hence momentum will increase proportionately because momentum = mv so momentum is proportional to velocity.

But I can see that the graph is wrong because the line does not pass through ZERO. To pass through ZERO it has to be a curve.

Is it meant to be a curve because gravity comes into play? Gravity means acceleration and that is metres per second 'squared'. The 'squared' bit produces the curve.

No readings are possible between 0 - 15 cm because the trolley is slowed by friction. Would the experiment be better done on a ramp made of ice and an ice cube trolley. Might that produce a curved graph?