What is the relationship between the acceleration and the angle of the slope?

[Ocis]

Homework Statement

To calculate the kinetic friction of a block of wood and determine its acceleration by timing it as it travels down a slope. The equipment available consists: of a plank of wood, clamps etc. for raising one end of it to give an inclined plane, blocks to slide down the plane, weights which may be attached to the blocks, measuring equipment, and a timer.Can this be achieved without knowing the mass of the blocks? Because despite being allowed to use weights the equipment doesn't mention digital scales...
Known data: height & distance (slope), time, angle(Ө), acceleration. Us (static coe.)

Homework Equations

Us = TanӨ (Ө being angle of slope)
Uk = Ff= P+mgsinӨ (P =Applied Force)
Nf mgCosӨ

The Attempt at a Solution

I have already completed the results to get the Us (static coefficient) = TanӨ . I know that if the weight of the block is doubled so will the frictional force, but I am unsure how the acceleration helps to solve the Uk? Have I missed something? Thanks.

 

[Doc Al]

For the case of a block accelerating down the slope, identify the forces acting and apply Newton's 2nd law. (Draw the usual free body diagram.) That might help you understand how measuring the acceleration allows you to calculate the coefficient of kinetic friction.

 

[Ocis]

I know that the acceleration is directly proportional to the net force, and that the forces are therefore unbalanced to create an acceleration. I have drawn a f.b.d. but I am struggling to appreciate what good acceleration is without a mass or force to calculate the Uk...? Anymore clues or suggestions would be appreciated..

 

[tiny-tim]

Welcome to PF!

I have drawn a f.b.d. but I am struggling to appreciate what good acceleration is without a mass or force to calculate the Uk...?

Hi Ocis! Welcome to PF!

The acceleration perpendicular to the slope is zero, so the normal force is the same as before.

Then just use Newton's second law for forces parallel to the slope.

You don't need to know the mass, because mass will be in all the forces on the left-hand-side, and you should have mass x acceleration on the right-hand-side.

So just divide the whole equation by mass!

 

[Ocis]

I would love to say I understand but I am even more confused now... What formula/equation are you referring to exactly. I can appreciate that the normal force is the same but its determining the applied force from just an acceleration? Am I expected to work this out from just having values of acceleration, angle, gravity? Sorry...

 

[tiny-tim]

What formula/equation are you referring to exactly.

Hi Ocis!

Total force along the slope = mass x acceleration along the slope.

In other words: mgsinθ - µN = m x acceleration.

So µ = … ?