A cart of mass m = 0.84 kg on a track undergoes a collision with another cart. It's velocity before and after the collision, vi and vf is measured and found to be vi = 1.32±0.04 m/s and vf = 0.30±0.04 m/s. If the collision lasts a time interval Δt = 0.100±0.006 s, calculate the average force Fave = Δp/Δt. how do you calculate the standard deviation of Fave?

Question

A cart of mass m = 0.84 kg on a track undergoes a collision with another cart. It's velocity before and after the collision, vi and vf is measured and found to be vi = 1.32±0.04 m/s and vf = 0.30±0.04 m/s. If the collision lasts a time interval Δt = 0.100±0.006 s, calculate the average force Fave = Δp/Δt. how do you calculate the standard deviation of Fave?

Answer 1

The relative standard deviation is

(ÄF)/F = sqrt[(Äp/p)^2 + (Ät/t)^2]

For Äp, you need to consider the uncertainties in both initial and final velocities. The initial and final momentum error terms add as the root sum of squares (RSS).

Äp^2 = M^2[Ävf^2 + Ävi^2]

put those two equations together to solve for ÄF