A crate of bananas with a mass of 50kg rest on a loading ramp that makes an angl

Question

A crate of bananas with a mass of 50kg rest on a loading ramp that makes an angle theta = 30 degrees with the horizontal ground. The coeeficient  of ststis friction is Mu2 =0.6 and the static kinetic friction is Mu2 =0.4

What is the maximum static friction force possible between the box and the ramp?

What is the static friction force on the box to keep it from sliding?

Is the crate able to remain at rest or will it begin to slide?

If you were to give the crate a shove down the ramp (to get it going) would it speed up, slow down, or move  at a constant velocity as it slides down the ramp?

Please explain your answers

Explanation / Answer

Maximum Static Friction = Mu2*mg*Cos(theta)

= 50*9.8*0.6*Cos(30 degree)

= 254.611 N

static friction force on the box to keep it from sliding = Mu2*mgCos(theta)

= 0.4*50*9.8*Cos(30 degree)

= 169.74 N

Here

Force down the place = mgSin(theta)

= 50*9.8*Sin(30 degree)

= 245 N

As

Maximum Force of Static Friction > Downward Force

So it Will remain at REST

It will Slow Down as Net Force is against the Motion

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