Forces Lab: Cart and pulley. I attempted to find acceleration using 4 kinematic

Question

Forces Lab: Cart and pulley. I attempted to find acceleration using 4 kinematic equations and came up with 4 completely different answers. I am unsure if my way of manipulating the formulas to solve for acceleration was correct. May someone assist with questions 3-8 ( which will in turn fill in the chart) based on the following values:

Mass = .5147 kg

Theta = 2.35

Theoretical = mgsin(theta) = .207

intitial time = .60 s

initial postion = .172 m

initial velocity = .1540 m/s

final time = 2.30 s

final postion = 1.130 m

final velocity = .3285 m/s

difference in time = 1.7 s

3. From the initial and fi nal properties, there are 4 kinematic equations that can be used to 4. 5. 6. 7. calculate the acceleration. What are these 4 equations? Use each equation to get 4 values for the acceleration. Calculate the average of the 4 accelerations and the standard deviation. From the average acceleration, calculate the experimental net force. How do the theoretical and experimental net forces compare? Explain why (are the assumptions the same?). Calculate the force of friction on the ramp. 8. angle 1 angle 2 t Theoretical 161 ai average a- Di 5 6-1 Experimental F

Explanation / Answer

given mass M = 0.5147 kg
theta = 2.35 deg
intitial time = .60 s
initial postion = .172 m
initial velocity = .1540 m/s
final time = 2.30 s
final postion = 1.130 m
final velocity = .3285 m/s
difference in time = 1.7 s

theoretical acceleration, a = gsin(theta) = 9.81*sin(2.35) = 0.40224 m/s/s

now, using, v = u + at
0.3285 = 0.1540 + a*1.7
a1 = 0.10264 m/s/s

using d = ut + 0.5at^2
1.130 - 0.172 = 0.1540*1.7^2 + 0.5*a*1.7^2
a2 = 0.3549 m/s/s

using
2*a*d = v^2 - u^2
2*a*(1.130 - 0.172) = 0.3285^2 - 0.1540^2
a3 = 0.06398 m/s/s

using
v = (d - 0.5at^2)/t + at = d/t - 0.5at
0.3285 = (1.130-0.172)/1.7 - 0.5*a*1.7
a4 = 0.1995 m/s/s

so aav = (a1 + a2 + a3 + a4)/4 = 0.1995 m/s/s

so the theoretical and all other accelerations are diffent, probably because error in measurements

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