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M2 Question - Friction/Plank

Any help is appreciated as I have spent quite a while figuring out where to start.

Uniform plank of 200N and length 2m rests on a smooth step of height 0.2m with one end of the plank lying on rough horizontal ground. Plank is in equilibrium and makes an angle of 10 degrees to horizontal.

Find least possible coefficient of friction between plank and ground.

I know F=uR will be needed and obviously have to find out F and R to work out u but finding F and R is what I'm struggling with.

First part of the question was to show force which plank exerts on the step is 171N, I'm not sure I did that right either :frown:

Thanks in advance!

Reply 1

ttoby

I would agree with your 171N.

What you can do now is resolve horizontally to get an equation involving F and the horizontal component of your 171N.

Then resolve vertically to get another equation involving R, the weight and the vertical component of your 171N.

Reply 2

Harfarin

Haha unfortunately the question was "show that it is 171N" so the 171N is correct but my method of finding it was...interesting.
Nevertheless, thanks for your guidance, worked out distance is 1.134m and trying to take moments about the point as we speak.

Reply 3

ttoby

Sorry, I just realised that although you could take moments, it is simpler to resolve horizontally then vertically. I've edited my post above to reflect this.

Reply 4

Harfarin

ttoby

Sorry, I just realised that although you could take moments, it is simpler to resolve horizontally then vertically. I've edited my post above to reflect this.

Don't apologise! It's already great of you to help me so much.

I've resolved vertically to get R = 200N + 171sin10
F = 171cos10, previously i thought F was acting inwards (towards step) but for this to be true, there must be a force im missing or the 171cos10 is not acting to the right as I thought.
This seems very basic for a 6 mark question however, and I'm confused about where exactly the 171N is. Am i right in thinking it is where the plank meets the step in \ direction with the arrow going downwards not upwards.

Edit : Ah i think I'm missing the 200cos10 from my resolve lines, I'll recheck

Reply 5

ttoby

The 171N would have to be pointing up and away from the step, but exactly perpendicular to the plank. This means that there will be an angle of 10 degrees between the 171N and the vertical. So the horizontal component of that force will be 171sin10 and the vertical component will be 171cos10.

Regarding the length of the question, there should be a few marks allocated for finding F and R, then a few more for using these values to get the minimum value of mu.