Coefficient of Kinetic Friction Question

[craig.16]

Homework Statement

A box is held on a rough plank inclined at an angle of 60° to the horizontal. The box is
released from rest and slides down the plank with a constant acceleration of 5 m/s2. Calculate
the coefficient of kinetic friction between the box and the plank.

Homework Equations

f(k)=mu(k)*N

The Attempt at a Solution

I got:
N=mgcos60=9.81mcos60
F(k)=masin60=5msin60
then rearranged above equation to mu(k)=F(k)/N to give me (500/981)tan60 which came to 0.88 (2dp). Just need to know if my answer is right or if I messed up somewhere.

 

[tiny-tim]

hi craig!

(have a mu: µ )

N=mgcos60=9.81mcos60

that's fine

F(k)=masin60=5msin60
then rearranged above equation to mu(k)=F(k)/N to give me (500/981)tan60 which came to 0.88 (2dp).

no, i don't follow that

what is your F_total = ma equation?

 

[craig.16]

since the N is perpendicular to F when F=ma and a=5, if N=mgcos60=9.81mcos60 then F would be:
F=masin60=5msin60 and using the coefficient of kinetic equation mu(k)=F/N that goes to (500/981)tan60 giving me 0.88. Are you just confused about how I got it or am i just completely wrong or going off track here lol. Oh and the F(k) is the F(total).

 

[tiny-tim]

Is your F the total force (down the slope), or only the friction force?

It seems to be both.

 

[craig.16]

F is the total force.

 

[Beaker87]

The two forces parallel to the incline are:

The parallel component of the gravitational force
and
The frictional force.

When added together, these two forces should equal the total force.

To get the total force, multiply the mass times the acceleration down the incline.

 

[craig.16]

Sorry your right I jumped to far ahead without thinking. I tried again and got

Spoiler

0.71

. Is this the right answer?

 

[tiny-tim]

that looks about right

but why haven't you shown how you got it?

exam marks aren't all for the right result, the way you get it matters too

 

[craig.16]

Thanks for the help. I'll make sure next time to include my working out, I know it needs to be done in the exam but for some reason I decided to post just the answer here. Always good to be notified though as a reminder.