A 500-gram block, resting on a level floor is pressed against a horizontal sprin

Question

A 500-gram block, resting on a level floor is pressed against a horizontal spring, compressing it 8cm The force constant of the spring is 300N/m. If the coefficient of kinetic friction between block and floor is 0.300, how far will the block slide before coming to rest? A 500-kg crate is pulled across a warehouse floor by means of a horizontal cable connected to an engine The coefficient of kinetic friction between the crate and the floor is 0 450. How much power must the engine deliver in order to move the crate at a constant speed of 4m/s?

Explanation / Answer

8) m =500 g, xi = 8cm, k =300 N/m, uk =0.3

Work done by nonconservative force is change in mechanical energy

Wnc = (Kf+Uf) - (Ki+Ui)

-(Fk .xf)  = Uf -Ui

-uk*mg*xf =(1/2)kxf^2 -(1/2)kxi^2

(1/2)kxi^2 = (1/2)kxf^2 +(uk*mg*xf )

(1/2)(300)(0.08*0.08) = (1/2)(300)xf2 +[0.3*0.5*9.8*xf]

0.96 = 150xf2 + 1.47xf

150xf2 + 1.47xf -0.96 =0

xf = 0.07 m =7 cm

xf = - 0.085 m =8.5 cm

xf value is less than 8 cm

xf = 7 cm

9) m = 500 kg, uk =0.45, v = 4m/s

Fk = uk*mg = 0.45*500*9.8 = 2205 N

P = F.v = 2205*4

P = 8820 W

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