Physics impulse and momentum lab help

[bowlfrog]

Okay so we have an impulse and momentum lab and I have to do the data analysis for my group. Usually I find the data analysis calculations a cathartic processes but I am totally stuck for this one. I am in a calc based physics lvl 1 course dealing in Newtonian mechanics. Anyway for the lab we had to roll a cart down an inclined plain and use computer software to calculate
collision time (interaction time), momentum, force of impact, and impulse. At the bottom of the plain and attached to the cart were opposing magnets, and we recorded the data for the first 4 "bounces". The issue I run into is this: I am supposed to calculate the impulse using ΔP of our data, and the percent difference of computer calculated impulse and ΔP calculated by us. Then I am supposed to use the mass of the cart and stuff to find the impulse due to gravity, use that to correct my impulse calculation, and then calculate the new average % diff of I and ΔP.

Homework Equations

I=ΔP=Mv₂-Mv₁
% diff of impulse and ΔP = [|FΔt-|ΔP||/(FΔt)]χ100%

Data collected:
Angle (radians) = θ
Acceleration = a = 0.215m/s²
Cart Mass= m_c
Additional mass= m_b
Mass of system = m_c+m_b = M
Initial time = t₁
Final time = t₂
duration of collision = Δt
impulse (FΔt) = I_o
Computer calculated impulse=I
Initial momentum = P₁
final momentum = P₂

The Attempt at a Solution

When I did it the first time I just subtracted the impulse found in the first part with the impulse I calculated due to gravity. So I just did this,
F_g = M(-9.8)
I_g = FΔt
I used the Δt we recorded from our first data.
then I did
I_o-I_g to get the new impulse I_f

The problem is when I calculated the percent difference it was larger with the "correction" Originally my avg % diff was 6.667%, but the second time it was around 22%. I know I must have messed something up. Maybe I should've taken the incline into account? I would really appreciate it if I got help here soon. I have to hand it over to my other lab partner sometime today and he's kind of a tool. if I have to wait a few, I am okay with that. He can just deal with it, or I can just do the whole lab analysis myself. Thank you SO MUCH!

*edit* I just attached my data in an excel document if anyone needs that

 

[AvroArrow]

. Solution:You are correct that you should take the incline into account. When calculating impulse due to gravity, the force of gravity should be replaced by the component of gravity in the direction of the incline. This is because the cart will be accelerating down the incline and not just straight down. The component of gravity in the direction of the incline will be given by Fgcos(θ), where θ is the angle of the incline. Therefore, the impulse due to gravity will be Ig = Fgcos(θ)Δt. You can then use this value to calculate the corrected impulse If by subtracting Ig from Io. Finally, you can then find the new percent difference by using the formula: % diff of impulse and ΔP = [|FΔt-|ΔP||/(FΔt)]χ100%Hope this helps!