2 Main Question A block weighing 80 N is subject to a force F di- rected directl

Question

2 Main Question A block weighing 80 N is subject to a force F di- rected directly up the slope, as shown to the right. The coefficients of static and kinetic friction that the block makes with respect to the surface are s 0.25 and 0.15, respectively. 20° a) What is the minimum magnitude of the force F to keep the block from slipping down the slope? b) What is the maximum magnitude of the force F before the block begins moving up the slope? c) What magnitude should the force F have to make the block accelerate at a rate of 2.0 m/s2 immediately after the block begins moving?

Explanation / Answer

Here,

a) theta = 20 degree

for the minimum magnitude of force F

minimum magnitude of force F = m*g * sin(theta) - u * mg * cos(theta)

minimum magnitude of force F = 80 * (sin(20 degree) - 0.25 * cos(20 degree))

minimum magnitude of force F = 8.7 N

b)

for the maximum magnitude of force F

maximum magnitude of force F = m*g * sin(theta) + u * mg * cos(theta)

maximum magnitude of force F = 80 * (sin(20 degree) + 0.25 * cos(20 degree))

maximum magnitude of force F = 46.2 N

c)

for the acceleration = 2 m/s^2

force needed = 80/10 * 2 + 46.2

force needed = 62.2 N

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