A force F acting on a particle of mass 5 kg placed on a smooth horizontal surface. F = 40 Nt remains constant but its vector rotates in a vertical plane at an angular speed 2 rad/sec. If a t = 0 , vec

Question

A force F acting on a particle of mass 5 kg placed on a smooth horizontal surface. F = 40 Nt remains constant but its vector rotates in a vertical plane at an angular speed 2 rad/sec. If a t = 0 , vector F is horizontal, find the velocity of block at t = π /4 ω sec.

TestHub · Accepted Answer

Only the horizontal component of F moves the block on the smooth surface: F x ​ = F cos ω t . a = m F cos ω t ​ = 8 cos 2 t m/ s 2 . v = ∫ 0 t ​ 8 cos 2 t d t = 4 sin 2 t . At t = 4 ω π ​ = 8 π ​ : v = 4 sin 4 π ​ = 2 2 ​ m/s .

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