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Coefficient of friction help!

A particle is projected with an initial speed of 8m/s across a rough horizontal surface and comes to rest 10m from its starting point.

Calculate the coefficient of friction between the particle and the surface.

Okay, so far I've worked out the acceleration using v^2=u^2+2as and I worked this out to be -3.2 which makes sense as it's slowing down.

But I'm not sure what else I need to work out or do to enable me to find the coefficient of friction as ideally I would need to know the mass of the particle so that I can find R but I'm not sure how I can find this.

Any help would be much appreciated thank you! :smile:

Reply 1

the bear

you can now work out the friction force using F = ma

once you know the friction you can find the coefficient of friction in the usual way.

Reply 2

leverarch

Original post by the bear

you can now work out the friction force using F = ma

once you know the friction you can find the coefficient of friction in the usual way.

I'm not sure how I would know the value of F or m?

Reply 3

Ben-2000

use coefficient of friction = a/g and use the value of a you found from SUVAT

Reply 4

leverarch

Original post by Ben-2000

use coefficient of friction = a/g and use the value of a you found from SUVAT

not heard of this equation before - I'm doing a level maths, what does a/g stand for?

Reply 5

RDKGames

Study Forum Helper

Original post by leverarch

I'm not sure how I would know the value of F or m?

There is only a frictional force of

-\mu R

acting in the opposite direction to motion. We can denote

R = mg

and hence the frictional force is

-\mu mg

.

Due to N2L, as this is the only force acting on the particle, we have that it's equal to

ma = -3.2m

.

Hence you have

-\mu m g = -3.2 m

Reply 6

leverarch

Original post by RDKGames

There is only a frictional force of

-\mu R

acting in the opposite direction to motion. We can denote

R = mg

and hence the frictional force is

-\mu mg

.

Due to N2L, as this is the only force acting on the particle, we have that it's equal to

ma = -3.2m

.

Hence you have

-\mu m g = -3.2 m

sorry really dumb question but what does N2L mean?

Reply 7

RDKGames

Study Forum Helper

Original post by leverarch

sorry really dumb question but what does N2L mean?

Newton's 2nd Law (of motion)

Reply 8

Ben-2000

I'm doing A-level maths as well. It's not an equation you're given but you derive it from F = ma and F = (Mu)R.

You can then say ma = (Mu)R

Substitute R as R = mg

ma = (Mu)mg

Mass then cancels and rearranging gives Mu = a/g, where a = acceleration and g = gravity.

In this case that formula works but it doesn't always work, (normally when you're resolving with more than one force) but idk the exact rule

PS: Mu = coefficient of friction represented by the Greek letter, pretty sure it's pronounced "Mu" aha 😂