You have a light rope being pulled horizontally that is going over a pulley and

Question

You have a light rope being pulled horizontally that is going over a pulley and pulling a 15kg mass up a 35 degree incline. Friction on the incline is .3 and the pulley is a solid disc with a radius of 2m with a mass of 4kg. If you wanted the box to accelerate up the incline 9.8m/s^2 how much force is needed to be applied to the rope You have a light rope being pulled horizontally that is going over a pulley and pulling a 15kg mass up a 35 degree incline. Friction on the incline is .3 and the pulley is a solid disc with a radius of 2m with a mass of 4kg. If you wanted the box to accelerate up the incline 9.8m/s^2 how much force is needed to be applied to the rope

Explanation / Answer

Tension in the rope is F = m*g*sin(theta) + (mu_k*m*g*cos(theta))

F = (15*9.8*sin(35))+(0.3*15*9.8*cos(35)) = 120.44 N

Using Torque acting on the pulley is T = I*alpha

I = 0.5*mp*Rp^2 = 0.5*4*2^2 = 8 kg-m^2

alpha = a/R

then

T = R*F = I*(a/R)

2*F = 8*(9.8/2)

F =19.6 N

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