The method and the results are on the conservation of energy lab. Do the analysis yourself first, then check the answers below.
Quick answer: Conservation of energy says the total energy of an isolated system stays constant: energy changes form, such as gravitational or spring potential energy becoming kinetic energy, but is never created or destroyed. These answers go with the AP Physics 1 lab on conservation of energy: the graph, the calculations, the uncertainties and the conclusion explained, for all 8 analysis questions.
The model answers use the sample data in the results table. Your own values will differ, but the method and the reasoning about uncertainty and efficiency should match.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 3
Question 2 Uncertainty in time
Walking: range = 14.8 − 14.2 = 0.6 s, so uncertainty = 0.3 s, which is 0.3 ÷ 14.5 = 2.1 %. Running: range = 8.2 − 7.8 = 0.4 s, so uncertainty = 0.2 s, which is 0.2 ÷ 8.0 = 2.5 %. The running time has the larger percentage uncertainty.
Question 3 Walking power
P = ΔU ÷ t = 1991 J ÷ 14.5 s = 137 W.
Question 4 Running power
P = 1991 J ÷ 8.0 s = 249 W.
Question 5 Same work, different power
The climber gains the same energy because the vertical height and the mass are unchanged. Running does that job in less time, so the power is higher: 249 ÷ 137 = 1.8 times greater.
Question 6 Body efficiency
Echem = useful energy ÷ efficiency = 1991 J ÷ 0.25 = 8.0 × 10³ J. The remaining 75 % (about 6.0 × 10³ J) is transferred as thermal energy to the body and surroundings, which is why the climber feels hot.
Question 7 Sources of error
Reaction time in starting and stopping the timer adds or removes a few tenths of a second, so power may be too high or too low (random). The climber also gains kinetic energy and may swing the arms, and the step height measurement may be a little off; ignoring these makes the calculated power slightly too low. Reaction time is the largest error.
Question 8 Improving the lab
Use light gates or two helpers with timers at the start and finish, and measure the height of the whole staircase with a long tape. Increase the number of trials, or use a taller staircase so that the timing error is a smaller fraction of the total time. These reduce the percentage uncertainty.
