Acceleration and velocity of cart travelling down an inclined plane.

[tranced]

I'm having problems of calculating the acceleration and velocity of a cart traveling down an inclined plane. I also need help calculating Sin theta. I've used 2 formulas to try calculating the acceleration and i get different answers. the first formula is a=2s/t2(squared), the 2nd formula was a=gsintheta. As for the angle sintheta i used the height of the plane/length of the board but i get ridiculous answers.

Length of inclined plane: 150.5cm
Point at which the cart is released: 115cm
Weight of cart: 784.30g

1st, height of the plane was 10 cm, avg time was 2.573 a=? v=?
2nd, height 20cm, avg time 1.483 a=? v=?
3rd, height 30cm, avg time 1.1783 a=? v=?
4th, height 40cm, avg time 0.973 a=? v=?
5th, height 50cm, avg time 0.8716 a=? v=?
6th, height 60cm, avg time 0.783 a=? v=?
7th, height 70cm, avg time 0.723 a=? v=?
8th, height 100cm, avg time 0.58 a=? v=?

Would appreciate it very much if someone could help me. I've been stuck at this for a week now and its getting really frustrating. Thank you!

 

[Delphi51]

Welcome to PF, tranced!

When the height is 10 cm, sin(θ) = 10/150.5
Have to do inverse sine of each side to get θ = inverse sin(10/150.5).
That works out to about 4 degrees for θ.
Looks like the theoretical g*sin(θ) formula gives an acceleration about twice as great as the experimental a=2s/t². This is not surprising; in practise friction and rotation of the wheels will reduce the expected acceleration.

You could get the average velocity easily with v = d/t, but I think you need the final velocity. Do you know how the final velocity is related to the average velocity for constant acceleration problems?
If not, you can probably see it on a sketch of the velocity vs time graph.

You have quite a few measurements; I suggest a table with columns for d, t, θ, g*sin(θ) and 2s/t². You could do it on a spreadsheet to have the calculations done automatically.

 

[tranced]

Thanks very much for your help Delphi. Appreciate it. You been great help :)

 

[tranced]

I'm still unsure how i can find the velocity. The cart's initial velocity is 0. But i have the acceleration, time and distance. which formula should i apply to find our the velocity?

 

[Delphi51]

The velocity increases steadily so the v vs t graph is a straight line from (0,0) to (t,Vf). The triangular area under this graph is
d = ½*b*h = ½*t*Vf
so Vf = 2d/t to calculate the final velocity from your time and distance measurements.

The theoretical final velocity is found from the usual
Vf = Vi + a*t