Betty is attempting to slide a sofa across a wooden floor. The sofa has a mass o

Question

Betty is attempting to slide a sofa across a wooden floor. The sofa has a mass of 130 kg and has legs made of wood. Betty pulls forward on a rope attached to the sofa with a maximum force of410 N, but fails to move it. She calls Ann for help. (Quote your answers using 3 sig figs.) a) What is the minimum additional force with which Ann has to push horizontally from the back of the sofa in order to overcome static friction and move the sofa? b) After the sofa is in motion, what is the total horizontal force that must be provided by the team of Ann and Betty to keep the sofa moving at constant velocity?

Explanation / Answer

here,

mass of sofa , m = 130 kg

us = 0.5 , uk = 0.2

force Betty , Fb = 410 N

a)

let the additional force be F

equating the forces

( F + Fb) = us * ( m *g)

( F + 410) = 0.5 * ( 130 * 9.81)

F = 227.65 N

b)

let the force required be F

F = uk * ( m * g)

F = 0.2 * 130 * 9.81 N

F = 255.06 N

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