Question

A crate of mass m₁ = 11.4 kg is pulled by a massless rope up a 36.9° ramp. The rope passes over an ideal pulley and is attached to a hanging crate of mass m₂ = 16.3 kg. The crates move 2.70 m, starting from rest. Find the final speed of the sliding crate if the incline is frictionless.

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Explanation

Since energy is conserved and nonconservative forces do no work, mechanical energy is conserved. Let the y-axis point straight upward.

Answer 1

solution mi= 11.4 kg m₂ = 16.3 kg Q = 36.90 Let and acceleration tension be of system be I then a m2 g - Ta mza 16-3 x 9.81 - T 16-3 Xa T- 11.4 x 9.81 x Sin 36.90 - - 11.49 ☺ 16.3 *9.81 – 11.4 *9.81 x Sin 36.9 = (16.3 +11-4) a = 3.35 m/s2 so using v² u²tzan J 2X 335 x 2-70 = 4.25 mls By another method change in PE of Box M₂ 1. = gain of ke of Box m, endom + gain inpe of m, 16-3 x9-81 x 2.70 =\x{16-3 +11.4) v2 11.489-81 X 2.70 x sin 36.90 =) v²= 18.08 v=v18.08 = 4.25 m/s