# M1 Forces question

An object resting on a rough surface is attached to a rope at 30 degrees to the horizontal. The rope is pulled with a force of PN. The mass of the object is 5kg.

(A) Draw a diagram showing all the forces acting on the object. Describe the origin of each force using words.

B) By resolving forces in the horizontal and vertical directions, calculate the magnitude of each force in the diagram, giving your answers in terms of P where appropriate.

C) If P=20, the object does not slip. Use this information to give a bound on meu in the form of an equality.

I've got A), B) and almost C.

I've got meu in the last question by resolving vertically to find R and then horizontally(resultant force is 0) to solve meu. I just don't get the inequality sign to use. The mark scheme says meu>=0.44, what's the reason?
Original post by dont know it
An object resting on a rough surface is attached to a rope at 30 degrees to the horizontal. The rope is pulled with a force of PN. The mass of the object is 5kg.

(A) Draw a diagram showing all the forces acting on the object. Describe the origin of each force using words.

B) By resolving forces in the horizontal and vertical directions, calculate the magnitude of each force in the diagram, giving your answers in terms of P where appropriate.

C) If P=20, the object does not slip. Use this information to give a bound on meu in the form of an equality.

I've got A), B) and almost C.

I've got meu in the last question by resolving vertically to find R and then horizontally(resultant force is 0) to solve meu. I just don't get the inequality sign to use. The mark scheme says meu>=0.44, what's the reason?

If the coefficient of friction is greater than or equal to the crtiical value, the object will not slip. That's all it is saying.
Original post by mqb2766
If the coefficient of friction is greater than or equal to the crtiical value, the object will not slip. That's all it is saying.

Oh I see, thanks. Could you help me this question too please?

An object of 3kg sits on a plane inclined at an angle theta to the horizontal. The coefficient of friction between the object and the plains is meu. The system is in limiting equilibrium.

A) Draw a diagram showing all the forces acting on the object. Describe the origin of each force using words.

B) By resolving forces in two perpendicular directions, show that meu is tan theta

C) hence, determined. Whether or not the object slips meu is 0.3 and theta is 30 degree

I've got A) and B), but I'm not sure my method's right for C.

I resolved perpendicular to the surface to find the normal reaction. Then I resolved parallel to the surface. 3gsin30-0.3(3gcos30) > 0 therefore the object slips. Is that correct?
Original post by dont know it
Oh I see, thanks. Could you help me this question too please?

An object of 3kg sits on a plane inclined at an angle theta to the horizontal. The coefficient of friction between the object and the plains is meu. The system is in limiting equilibrium.

A) Draw a diagram showing all the forces acting on the object. Describe the origin of each force using words.

B) By resolving forces in two perpendicular directions, show that meu is tan theta

C) hence, determined. Whether or not the object slips meu is 0.3 and theta is 30 degree

I've got A) and B), but I'm not sure my method's right for C.

I resolved perpendicular to the surface to find the normal reaction. Then I resolved parallel to the surface. 3gsin30-0.3(3gcos30) > 0 therefore the object slips. Is that correct?

You're not wrong, but from B) you have
meu = tan(theta)
tan(30) = 0.577, meu = 0.3. Its not large enough to hold the system in equilibrium.

You can see this from your extra equation as you divide through by cos(30), cancel the 3g, and pop the meu over the other side. Easier to use B) though.
...

edit: oh, mqb2766 has already done it. my bad.
Please, no more meu'ing. It's "mu", the 12th letter of the greek alphabet.
Original post by mqb2766
You're not wrong, but from B) you have
meu = tan(theta)
tan(30) = 0.577, meu = 0.3. Its not large enough to hold the system in equilibrium.

You can see this from your extra equation as you divide through by cos(30), cancel the 3g, and pop the meu over the other side. Easier to use B) though.

Oh nice. How would you word this answer given it's 4 marks.

Would it just be tan30>meu and so there's a resultant force down the slope hence the object slides?
Original post by ghostwalker
Please, no more meu'ing. It's "mu", the 12th letter of the greek alphabet.

Ha yeah sorry. I just copied it from a thread in the past that is closed now.
Original post by ghostwalker
Please, no more meu'ing. It's "mu", the 12th letter of the greek alphabet.

Ha yeah sorry. I just copied it from a thread in the past that is closed now.
Original post by IslamJoynul
...

edit: oh, mqb2766 has already done it. my bad.

No worries, I still appreciate your effort.
Original post by dont know it
Oh nice. How would you word this answer given it's 4 marks.

Would it just be tan30>meu and so there's a resultant force down the slope hence the object slides?

Basically, yes. The question says "Hence" so its expecting you to use your previous answers. Four marks does seem a little over generous, but sometimes the reflection / interpretation is given a bit extra weight.

Edit - the question does illustrate a nice observation about the coefficient of friction. Basically, you can measure it by putting the object on an included plane and finding the angle at which movement starts. tan(theta) is therefore the coefficient of friction.
https://en.wikipedia.org/wiki/Inclined_plane
it also emphasises that the coefficient of friction can be > 1 (the angle at which movement starts is > 45 degrees). However, this would be unusual
(edited 5 years ago)
Original post by dont know it
An object resting on a rough surface is attached to a rope at 30 degrees to the horizontal. The rope is pulled with a force of PN. The mass of the object is 5kg.

(A) Draw a diagram showing all the forces acting on the object. Describe the origin of each force using words.

B) By resolving forces in the horizontal and vertical directions, calculate the magnitude of each force in the diagram, giving your answers in terms of P where appropriate.

C) If P=20, the object does not slip. Use this information to give a bound on meu in the form of an equality.

I've got A), B) and almost C.

I've got meu in the last question by resolving vertically to find R and then horizontally(resultant force is 0) to solve meu. I just don't get the inequality sign to use. The mark scheme says meu>=0.44, what's the reason?