An object with a mass of 6 kg lies on a horizontal surface with friction with a

Question

An object with a mass of 6 kg lies on a horizontal surface with friction with a coefficient of kinetic friction of 0.56 and a coefficient of static friction of 1.39. Two additional forces are applied to it. One force of 15 N directed at an angle of 36 degrees below the horizontal and another force in the +x direction. Originally, the force in the x direction is just enough to start to move the mass. If the 2nd force is then increased by a factor of 3, what is the acceleration of the mass in m/s2?

Explanation / Answer

in vertical,

N - m g - 15 sin36 = 0

N = 15 sin36 + (6x 9.81) =67.7 N

f_max = us N = 94 N

in horizontal,

Fnet = 15 cos36 + F2 - f_max= 0

F2 = 81.9 N

now 15 cos26 + 3 F2 - fk = m a

15 cos26 + (3 x 81.9) - (0.56 x 67.7) = 6 a

a =36.9 m/s^2

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