Linearising Graphs: Need Help with Height vs Velocity Relationship

[Yagami Edo]

I'm currently doing a lab on the relationship between height and velocity, however I am unable to linearise the graph. I'm not sure whether it should be root height vs velocity or height vs velocity squared. It would be great if someone could help me, thanks.

 

[jtbell]

I'm not sure whether it should be root height vs velocity or height vs velocity squared.

Either method should work, if you do it properly. The math might be simpler using one method. It depends on what information you want to extract from the graph, via the slope and/or y-intercept.

 

[BvU]

Hello Yagami, welcome to PF !

Will be glad to help, but you have to say a bit more of what this is about ! what is the experiment, what height, what velocity.
"root height vs velocity or height vs velocity squared"sounds like the same thing to me if there is no offset.
And perhaps it's height squared versus velocity (probably not, though ).

 

[Yagami Edo]

Thanks, for this lab we are to find the relationship between the velocity of a trolley moving down a ramp and the height of the ramp.

 

[BvU]

I'm currently doing a lab on the relationship between height and velocity, however I am unable to linearise the graph. I'm not sure whether it should be root height vs velocity or height vs velocity squared

OK, so the next question is: in what way are you unable to linearise ? You tried both ways and neither shows a perfectly straight line ? For every measurement point there are some uncertainties in speed and height to take into account - perhaps they spoil the picture becasue the errors are a bit big ? Or do the plots have distinctly nonlinear characteristics ?

 

[Yagami Edo]

The plots have distinctly nonlinear characteristics when attempting to linearise by squaring the velocity.

 

[BvU]

And you are familiar with the behaviour of $v^2$ as a function of $h$ as expected from the theory ?

 

[sophiecentaur]

I'm currently doing a lab on the relationship between height and velocity, however I am unable to linearise the graph. I'm not sure whether it should be root height vs velocity or height vs velocity squared. It would be great if someone could help me, thanks.

Either method should work, if you do it properly. The math might be simpler using one method. It depends on what information you want to extract from the graph, via the slope and/or y-intercept.

To get a straight line, all that's necessary is to plot the 'whole' of the left hand side of an equation with the 'whole' of the right side. The resulting points will all lie on a straight diagonal line. The difference between the resulting graphs is where the points will actually lie on this diagonal line. You can do virtually anything to both sides of the equation and you still get a straight line. What you choose to do will affect where the points actually lie on this line. They can be bunched up at one end or the other or spread out. You should choose which gives you the most suitable (for you) result.

I can recommend the use of a spreadsheet for this sort of graphing exercise. You can choose a whole range of graphs by choosing various columns, based on what you do with the original data columns. (It's a good intro to simple coding, too)

 

[Yagami Edo]

Thanks for all the replies, I'm not really aware of the behaviour of V squared as a function of h

 

[ZapperZ]

Thanks for all the replies, I'm not really aware of the behaviour of V squared as a function of h

Why don't you start by writing down ALL the kinematical equations that you do know at this level?

Zz.