A weightlifter performs an exercise in which he raises a mass of 200 kg from rest vertically through a distance of 0.7 m and holds it at that height.
(i) Find the work done by the weightlifter.
(ii) Given that the time taken to raise the mass is 1.2 s, find the average power developed by the weightlifter.
Solution
(i) The work done by the weightlifter is calculated using the formula for gravitational work done:
\(WD = mgh\)
where \(m = 200 \text{ kg}\), \(g = 9.8 \text{ m/s}^2\), and \(h = 0.7 \text{ m}\).
Substituting the values, we get:
\(WD = 200 \times 9.8 \times 0.7 = 1400 \text{ J}\)
(ii) The average power developed is calculated using the formula:
\(\text{Power} = \frac{\text{Work Done}}{\text{Time}}\)
Substituting the values, we get:
\(\text{Power} = \frac{1400}{1.2} = 1166.67 \text{ W}\)
Rounding to the nearest whole number, the average power is \(1170 \text{ W}\).
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