Question

To Önd the acceleration of a glider moving down a sloping air track, you measure its velocity at two points (v1 and v2); and the time t it takes between them: v1 = 0:21 0:05m=s v2 = 0:85 0:05m=s t = 8:0 0:1s (a) Assuming all uncertainties are independent and random, and acceleration is calculated using a = v2v1 t ; what should you report for a and its uncertainty? (b) You calculate using an air resistance model that the acceleration should be 0:13 0:01 m/s2 : Does your measurement agree with this prediction?

Answer 1

a = (0.08 ± 0.01) m / s²

Step-by-step explanation:

The average acceleration of a body can be calculated as the average speed in the time interval

a = Δv /Δt

a = (v₂ -v₁) / t

a) the acceleration value is

a = (0.85 - 0.21) /8.0

a = 0.080 m / s²

To calculate the uncertainty of an equation we use where we take the worst case scenario all the uncertainties add up

Δa = da/dv₂ Δv + da/dv₁ Δv₁ + da/dt Δt

Δa = 1 /t Δv₂ + 1 /t Δv₁ + (v₂ -v₁) 1/ t² Δt

Δa = 1 /t (Δv₂ + Δv₁) + (v₂-v₁) / t² Δt

Let's calculate

Δa = 1/8 (0.05 + 0.05) + (0.85-0.21) / 8² 0.1

Δa = 0.0125 + 0.001

Δa = 0.01 m/s²

The result of the acceleration is

a = (0.08 ± 0.01) m / s²

.b) The uncertainty found is in accordance with the air rail model used, but the value of the acceleration is much smaller, indicating the existence of some systematic error in the measurement