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Mechanics 2 m2 question

PaigeS1997

The question says:

A uniform lamina ABCD is in the form of a trapezium in which AB = AD =a, CD = 2a and angle BAD = angle ADC and = 90 degrees. (a) Find the distance of the centre of mass of the lamina from AD and from AB.

The lamina stands with the edge AB on a plane inclined at an angle alpha to the horizontal with A higher than B. The lamina is in a vertical plane through a line of greatest slope of the plane.

(b) Given that the lamina is on the point of overturning about B, find the value of tan alpha.

Hello, I've tried to do this question several times and I keep getting confused. Will someone please do the worked solution for me.

Thank you very much

(edited 8 years ago)

Reply 1

davros

Original post by PaigeS1997

The question says:

A uniform lamina ABCD is in the form of a trapezium in which AB = AD =a, CD = 2a and angle BAD = angle and = 90 degrees. (a) Find the distance of the centre of mass of the lamina from AD and from AB.

The lamina stands with the edge AB on a plane inclined at an angle alpha to the horizontal with A higher than B. The lamina is in a vertical plane through a line of greatest slope of the plane.

(b) Given that the lamina is on the point of overturning about B, find the value of tan alpha.

Hello, I've tried to do this question several times and I keep getting confused. Will someone please do the worked solution for me.

Thank you very much

Is there some information missing here?

I'm not good at visualizing this sort of thing - are you given any sort of diagram for this? What are the answers given for (a) and (b)?

Reply 2

PaigeS1997

Original post by davros

Is there some information missing here?

I'm not good at visualizing this sort of thing - are you given any sort of diagram for this? What are the answers given for (a) and (b)?

Sorry for the late reply. No there was diagram unfortunately. I am the same as you, I find it difficult to visualise what the question wants.

Reply 3

joostan

Original post by PaigeS1997

Sorry for the late reply. No there was diagram unfortunately. I am the same as you, I find it difficult to visualise what the question wants.

From your description, the trapezium should look like this only inverted, with the longest side being CD.
The centre of mass of the lamina can then be fond by combining the COM of the square and the triangle.
I haven't looked at the second part yet.

(edited 8 years ago)

Reply 4

davros

Original post by PaigeS1997

Sorry for the late reply. No there was diagram unfortunately. I am the same as you, I find it difficult to visualise what the question wants.

What about the bit I highlighted in bold - you seem to have missed out an angle or something there because it doesn't make sense!

And do you have the answers so we can check, assuming joostan's diagram is the correct interpretation?

Reply 5

joostan

Original post by davros

I think the OP was just explaining that BAD was an angle, though now you point it out I may be wrong.

Reply 6

davros

Original post by joostan

I think the OP was just explaining that BAD was an angle, though now you point it out I may be wrong.

I think your suggested diagram is the correct one, but I *think* we need slightly more information than given - either another side, or, more probably, another angle. You're probably right that the question implies there are 2 right angles in there, but I'd rather see the question explicitly before haring off and trying to solve things that don't work :biggrin: