The rope can withstand a breaking load of 1 ton. How long does it take to lift a 200 kg

The rope can withstand a breaking load of 1 ton. How long does it take to lift a 200 kg load from a mine 80 m deep?

To find the minimum time for lifting the load, we will use the formula: Fmax = m * a + m * g = m * (2S / t2) + m * g, whence we express: t = √ (m * 2S / (Fmax – m * g) ) = √ (m * 2S / (mmax * g – m * g)).

Variables and constants: m is the mass of the load being lifted (m = 200 kg); S is the depth of the mine (S = 80 m); mmax – maximum breaking load (mmax = 1 t = 10 ^ 3 kg); g – acceleration due to gravity (g = 9.81 m / s2).

Calculation: t = √ (m * 2S / (mmax * g – m * g)) = √ (200 * 2 * 80 / (10 ^ 3 * 9.81 – 200 * 9.81)) ≈ 2 s.

Answer: The minimum lifting time is 2 seconds.