Does any body know about mechanics (A level Maths)?

Question

I've got this question on forces and i dont know how to answer it. so if you know, please help!

A particle of mass 8000g is at rest in limiting equilibrium on a rough inclined plane, inclined at 40 degrees. Find the frictional force on the particle and the normal reaction and hence the coefficient of friction.

Im grateful for any help
thanks

Answer 1

well the first thing to do is to draw the situation. You have the ramp, the point mass and three forces.

The three forces are gravity, the normal reaction force and friction

The gravity force = mg and goes straight down
the normal reaction is perpendicular to the ramp (up-left ish)
the friction force is going up the ramp.

Now to keep the mass in equilibrium(not moving) the forces must be balanced which means that part of the force due to gravity is opposing each of the other two.

hence
the reaction force is = mg cos(40 degrees)
and friction = mg sin(40 degrees)

you can figure out which to use sin for by looking at your drawing and considering the angles in the triangles involved.

My memory is fuzzy about the exact equation using the coefficient of friction but I think it is

friction force = reaction force *coefficient of static friction

hence

coefficient of static friction = friction force/ reaction force
= mg sin (40) / mg cos (40)
= tan (40)

Hope this helps, good luck.

Answer 2

I can't really do the question justice without a diagram.

You need to resolve the forces into either horizontal or vertical components or in the direction of the plane and perpendicular to the plane.

There'll be the force of 8000g acting vertically down, a reaction at right angles to the surface, and friction acting up the plane. Remember the frictional force(F) is equal to the coeffiecient of friction multiplied by the reaction force (R).

Resolve horizontally, you get Fcos40=Rsin40
and vertically 8000g = Rcos40 + Fsin40 (I think)

The first equation lets you find F in terms of R and then substitue into the second equation, to get values.

Then, all you need to do is F divided by R to get the coefficient of friction. (Haven't got a trig calculator on me, so you'll have to do the working out!)

Answer 3

Draw a diagram.

Resolve the weight force into two components, one parallel to the inclined plane and one at right angles to the inclined plane.
The particle is in equilibrium, so the frictional force is equal and opposite to the component of the weight force parallel to the plane and the normal reaction is equal and opposite to the component of the weight force at right angles to the plane.

Coefficient of friction is the ratio of the two.

Answer 4

Hmmm.... limiting equilibrium ...The story of my life.

the friction force f= uN
u- coefficient of static friction
N - normal to the surface force exerted by mass m of 8000g (8 kg)mass
N=m g cos(angle of the incline)
where g is gravitational acceleration const 9.81m/s^2

As we intuitively know that the body just wants to move down pushed by the force generated due to its weight and parallel to the inclined F= W sin(angle of the inclined)
or F= m g sin(angle of the inclined)

Finally
f=F
u W cos(angle of the inclined)= W sin(angle of the inclined)
u=sin(angle of the inclined)/cos(angle of the inclined)
u=tan(angle of the inclined))
u=tan(40)=0.839


We did not even need the mass of the object after all.

Hope it was helpful.

Answer 5

I agree with Mike "the first answer'I was about to answer the same till I saw he had beaten me to it.So I should really be voted best answer

Answer 6

if youre having trouble with these and you'r doing the same boaard as i did you're fu**ed. you have to do these with pulleys and collisions, in combination with vuxat equations