Question

Raghav who weighs 55 kg records the time taken by him in running up a flight of steps on a staircase. He then measures the height of each step. He also counts the number of steps on the staircase. Following are his observations: Number of steps 28 Height of each step 20 cm Time taken 5.4 s Raghav’s mass 55 kg Acceleration due to gravity 9.8 m s−2

1. How much is the work done by Raghav?
2. What will be his power?
3. If Raghav’s friend, Ravi who weighs 50 kg runs up the stairs and takes the same time to reach the final position, who does the most work and develops the most power?
4. If another friend, Sameer who weighs the same as Raghav runs up the stairs in 10 s, who does the most work and develops the most power among the three friends?

Answer 1

Total height (h) = Number of steps × Height of each step

h = 28 × 20 cm = 560 cm = 56 m

(i) Work done by Raghav:

W = m × g × h

= 55 kg × 9.8 m/s² × 5.6 m

= 3018.4 J

(ii) Power developed by Raghav:

P = `"Work done"/"Time taken"`

= `(3018.4)/(5.4 s)`

= 558.96 W

(iii) Comparison between Raghav and Ravi:

• Work Done: Raghav has a higher mass (55 kg > 50 kg) climbing the same height. Therefore, Raghav does the most work.
• Power Developed: Since Raghav does more work in the exact same time (5.4 s), Raghav develops the most power.

(iv) Comparison among all three friends (Raghav, Ravi, and Sameer):

• Most Work Done: Raghav and Sameer both do the most work (3018.4 J each) because they have the same mass (55 kg) and climb the same vertical height.
• Most Power Developed: Raghav develops the most power (558.96 W). Sameer takes longer (10 s vs 5.4 s) to perform the same amount of work, which reduces his power output (301.84 W).