Practical Session 2: Ramp

Practical Session 2: Ramp(I)
Aim of the practical: calculate the acceleration that affects a ball falling down a ramp (with a constant slope) using the formulae for uniform acceleration motion in one dimension.
Theoretical Introduction: To ensure that our results are reliable we will firstly calculate the angle by the formulae: hL= tanθ.
Then to calculate the velocity, we will use the formulaewhere v=u+at, but considering that we are starting with a velocity of zero, u, will be Zero. Making the equation v=at. By this we can obtain the acceleration by: a= vt.
To prove that our results are reliable we are going to obtain the acceleration by the formulae s= ut + 1/2at² where the initial velocity is Zero:
s=1/2at². So:
s/t²= 1/2a→2s/t²= a
But we also have to calculate the uncertainties of our measurements.
We will have to use the formula when we are adding uncertainties (e.g. the uncertainty of our time of reaction timing the ball) of:
A=B+C
EA=EB+ EC
This means that the total error of a quantity (A) is the sum of the errors of the two measurements we are obtaining and adding (B, C).
But also if we multiply twoor more measurement we will use the formulae:
A=BC
→ EA%=EB%+EC%
→ E(A)A=E(B)B+ E(C)C
→ EA= E(B)B+ E(C)C A
This means that to obtain the total percentage error of the multiple of the measurements; we have to add both percentage errors ofthe measurements. To calculate the percentage error of a measurement we divide the uncertainty of one measurement by the measurement. After obtaining both percentage errors and adding them up, we would obtain the percentage error of the measurement. Then, to obtain the uncertainty and not the percentage error we multiply both measurements to obtain A, so then we add both uncertainties andmultiply it by the total measurement that would be A, giving the uncertainty error.
If we have a square root of an measurement is the same process but we can abbreviate it we doing twice the uncertainty:
A=L2
→ A=L x L
→ EA%=EL%+E(L)→ EA=2 E(L)L x A

We must take care, once you transform a percentage error into a total error, about getting only one significant figure.
Experimental method:
For this experiment we are going to use:
* A ramp adapted to ensure the correct path for the ball
* A wooden block where the ramp will be at rest to form a constant slope
* A ball
* A millimeter precision meterruler
* A time stop-watch
* A blocker to stop the ball when it arrives down the ramp
Steps followed:
Firstly we calculated the angle θ between the ramp and the table. To do this we had to measure the height of the ramp by measuring the height of the wooden block with the ruler. To gain accuracy we should measure the height of the wooden block when it is out of the ramp, so we can measureit easily. And then to calculate the length we will have to measure the length from where the ramp starts from wooden block starts till the end. We will measure the length by laying the ruler in the table to gain accuracy.
Then we will let the ball fall down the ramp for a distance of 100 cm, and time the time taken to reach this point. Then we will proceed to do the same but timing the timetaken for the ball 95 cm, and continue this process going 5 cm less till we reach 50cm.
Using the formulae we will calculate the value of the speed for each distance travelled, and then we will plot it in a graph. We will finish with two graphs as we used two different formulae. In the two graphs we should obtain the same gradient that will give us the acceleration that should be less than gravity...