at this time? (b) How much work is required to stop it? (c) What is the magnitud

Question

at this time? (b) How much work is required to stop it? (c) What is the magnitude of the constant force required to stop it as it undergoes a displacement of 2.50 km? 18. man pushing a crate of mass m-92.0 at a speed of 0.850 m/s encounters a rough horizontal surface of length e = 0.65 m as in Figure P5.18. If the coefficient of kinetic fric- tion between the crate and rough surface is 0.358 and he exerts a constant horizontal force of 275 N on the crate, find (a) the magnitude and direction of the net force on the crate while it is on the rough surface, (b) the net work done on the crate while it is on the rough surface, and (c) the speed of the 23. 24. crate when it reaches the end of the rough surface.

Explanation / Answer

(a) By F(net) = F(applied) - F(friction)
=>F(n) = 275 - µ x mg
=>F(n) = 275 - 0.358 x 92 x 9.8
=>F(n) = - 47.77 Newton [-ve indicating that it is a retarding force i.e. opposite the direction of motion]

(b) W = F(n) x s
=>W = 47.77 x 0.65 = 31.05 J

(c) By F = ma
=>47.77 = 92 x a
=>a = 0.52 m/s^2
By v^2 = u^2 - 2as
=>v^2 = (0.850)^2 - 2 x 0.52 x 0.65
=>v = 0.0465
=>v = 0.216 m/s

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