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In raising a 6200-n piano with a pulley system, the movers note that, for every 2.2 m of rope pulled down, the piano rises 0.12 m . ideally, find the force required to lift the piano.

The position of a crate sliding down a ramp is given by x=(0.05t^3) m, y=(1.7t^2) m, z=(6−0.85t^5/2) m, where t is in seconds. (a) determine the magnitude of the crate's velocity when t = 2 s. (b) determine the magnitude of the crate's acceleration when t = 2 s.

Alarge cruise ship of mass 7.00 ✕ 107 kg has a speed of 11.6 m/s at some instant. (a) what is the ship's kinetic energy at this time? (b) how much work is required to stop it? (give the work done on the ship. include the sign of the value in your answer.) (c) what is the magnitude of the constant force required to stop it as it undergoes a displacement of 3.00 km?