9a) Sergio needs to push a crate weighing 82.0 lb. If the coefficient of static

Question

9a) Sergio needs to push a crate weighing 82.0 lb. If the coefficient of static friction is µs = 0.600, with what force must he push to just start the chest moving?

9b) Once the box starts moving, the friction force transitions from static to kinetic friction. If the coefficient of kinetic friction is µk = 0.100, with what push must Sergio provide to move the crate with a speed of 2.00 ft/s?

9c) If the coefficient of kinetic friction is µk = 0.100, with what push must Sergio provide to accelerate the crate at 1.80 ft/s2?  

Explanation / Answer

a)
m = 82 lb = 37.2 Kg
F = force due to static friction
= µs*m*g
= 0.6*37.2*9.8
= 218.7 N
Answer: 218.7 N

b)
F = force due to kinetic friction
= µk*m*g
= 0.1*37.2*9.8
= 36.5 N
Answer: 36.5 N

c)
a = 1.8 ft/s^2 = 0.55 m/s^2
F - f = m*a
F - µk*m*g = m*a
F - 0.1*37.2*9.8 = 37.2*0.55
F = 56.92 N
Answer: 56.92 N

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