You are lowering two boxes, one on top of the other, down the ramp shown in the

Question

You are lowering two boxes, one on top of the other, down the ramp shown in the figure (Figure 1) by pulling on a rope parallel to the surface of the ramp. Both boxes move together at a constant speed of 18.0cm/s . The coefficient of kinetic friction between the ramp and the lower box is 0.460, and the coefficient of static friction between the two boxes is 0.755.

Part A

What force do you need to exert to accomplish this?

t.......n

Part B

What is the magnitude of the friction force on the upper box?

f.......n

You are lowering two boxes, one on top of the other, down the ramp shown in the figure (Figure 1) by pulling on a rope parallel to the surface of the ramp. Both boxes move together at a constant speed of 18.0cm/s . The coefficient of kinetic friction between the ramp and the lower box is 0.460, and the coefficient of static friction between the two boxes is 0.755. Part A What force do you need to exert to accomplish this? t.......n Part B What is the magnitude of the friction force on the upper box? f.......n

Explanation / Answer

Answer:  A) You're not accelerating so the force you need is only that required to overcome the weight force down the ramp PLUS the kinetic friction at the surface of the ramp.
Use the Ratios given to find out what part of the weight (of the two boxes combined) is acting perpendicular to the ramp. ie. the force Normal to the surface. and multiply this by the co-efficient to get the friction force.

You do this (part of weight) by drawing a triangle with weight downwards, split into Normal and parallel to surface.
This triangle will be Similar (in the maths sense) to the triangle of the slope in the picture, making this easier. Complete the triangle using pythagoras and then just use ratios. There's no need to get into Sin, Cos stuff.

B) The box is not slipping nor is it accelerating, so the static friction force is the minimum required to prevent it slipping down. i.e. Your friction force arrow up (the slope) will equal the weight force arrow down (the slope)
It's a fraction of the weight. Use the ratios.

C) Which way do you think the box would slip if it slipped? Friction force is in the other direction.

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