A student records a stair-climbing fitness test in a sports hall. Fig. 1 shows the student moving from the floor to a platform 3.2 m above it while carrying...
Question 1 Report
A student records a stair-climbing fitness test in a sports hall. Fig. 1 shows the student moving from the floor to a platform 3.2 m above it while carrying no equipment. The student's mass is 55 kg and the climb takes 6.0 s. The student repeats the test more quickly after warming up. Take g as 10 N/kg. The height is measured vertically, not along the sloping handrail.
(a) Calculate the weight of the student. [2]
(b) Calculate the gain in gravitational potential energy during the first climb. [3]
(c) Calculate the average power developed during the first climb. [3]
(d) Explain why a shorter climbing time gives a larger average power when the same student uses the same stairs. [2]
(e) State one energy transfer that occurs in the student's body and is not part of the useful gravitational potential energy gain. [1]
(f) Calculate the average power if the second climb takes 4.0 s. [2]
Answer Details
(a) \[W=mg=55\times10=550\text{ N}\] [2]
(b) Only vertical height matters for gravitational potential energy: \[\Delta E_p=Wh=550\times3.2=1760\text{ J}\] [3]
(c) \[P=\frac{E}{t}=\frac{1760}{6.0}=293\text{ W}\] Accept \(290\text{ W}\). [3]
(d) The same student climbing the same stairs gains the same gravitational potential energy. Completing this transfer in less time means a greater rate of energy transfer, so power is larger. [2]
(e) Some chemical energy is transferred to thermal energy in the student's body or surroundings, or to sound. [1]
(f) \[P=\frac{1760}{4.0}=440\text{ W}\] [2]
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