Practice for energy, momentum, and uncertainties

A brick of mass m = 2.55 +/- 0.03 kg sits at the top of a frictionless incline of height H = 1.21 +/- 0.01 m. Starting from rest, it slides down into an open cardboard box of mass M = 0.81 +/- 0.02 kg. The brick and box together then slide across a floor with coefficient of kinetic friction mu = 0.23 +/- 0.02 .

1. What is the speed v1 of the brick at the bottom of the incline? Include the uncertainty in this speed.
2. What is the speed v2 of the box-and-brick together just after the brick slides into the box? Include the uncertainty in this speed.
3. How far does the box slide before coming to rest? What is the uncertainty in this distance?
4. What is the single largest contributing factor to the uncertainty?

Condensed guide to propagate uncertainties

1. If you add or subtract two quantities, add the raw uncertainties in each measurement
2. If you multiply or divide two quantities, add the percentage uncertainties in each measurement to get the percentage uncertainty in the result
3. If you raise a quantity to power N, multiply its percentage uncertainty by N to get the percentage uncertainty in the result

For an example of what I expect, look at

• the analysis of a ballistic pendulum with uncertainties

You can find full guides in several places:

• Professor Lindberg's guide to using uncertainties
• My guide to using uncertainties

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.