how do u work out the coefficient of friction when the accelleration involved?

Question

a laundry basket of mass 3kg is being pulled by rope inclined at 30 degrees. tension in the rope = 8N. find the coefficient of friction when the acceleration is o.2 ms-2

Answer 1

The first thing to do to solve this problem is to draw a diagram showing all the forces acting on the system, ie.
1)the force of gravity downward
2)the forces applied by the rope, both horizontally(forward) and vertically (up) (the one force can be broken up into these two independant components. Check your textbook for a review on how to do this if necessary.)
3)the force of friction backward
4)the normal force upward

Then look at the equations at your disposal. We have
1)Newton's second law: Fnet=ma, the net force equals the mass times the acceleration.
2)Ff=(mu)Fn, the force of friction equals the coefficient of friction (represented by the greek letter 'mu') times the normal force
3)Fg=mg, the force of gravity equals the mass of the object times the gravitational constant (9.81ms^-2 at Earth's surface)

Now we remember Newton's First Law of Motion: in the absence of a net force, an object in motion will stay in motion, and an object at rest will stay at rest.

Since the object (a laundry basket in your case) is not moving vertically (it's sliding horizontally along the floor only), we can see that there is no net force vertically. Therefore all vertical forces (the force of gravity downward, the vertical part of the force of the rope upward, and the normal force upward) must add up to zero. up is positive, down is negative. Since you know the first two, you can find the third, Fn, or the Normal Force.

Remember that the equation that we need to solve is Ff=(mu)Fn. We now have Fn, so all we need to do is find Ff, or the force of friction, and we can solve for (mu). Almost there!

Since the laundry basket is moving forward, Newton's First Law says that there must be a Net Force on it. In other words, all the horizontal forces add up to a positive number (since the basket is moving forward). This Net Force equals the mass times the acceleration (Fnet=ma). You are given both m and a, so finding Fnet is just a matter of multiplication.

Now to figure out Ff:

Look at your horizontal forces: you have the horizontal component of the force from the rope 'pulling forward' and the force of friction (Ff) resisting the motion (ie 'pulling backward').

So the the 'force forward' minus the 'force backward' equals the net force, or F(rope, horizontal)-Ff = Fnet. The only one you don't know is Ff, so F(rope)-Fnet=Ff.

Now, using Ff=(mu)Fn, (Force of friction = coefficient of friction times the normal force) where we just found Ff and Fn, you can rearrange and solve for (mu). Done!

Answer 2

draw a free body diagram with all the forces acting on it, and the acceleration should equal the sum of all the forces divided by mass. Here:

friction < ----- Basket ----> T

with a normal force (n) upwards, and the mg pulling down,
where the acceleration would be in the direction to the right --->

so, what you would do is:

m*a = T - friction
(3kg)(0.2ms^-2) = 8N - (Uk)(n)
0.6 = 8 - (Uk)(mg)
Uk= 0.25 (approx)


oooh wait sorry, didnt notice the rope was inclined...:p

Answer 3

Resolving vertically: N + Tsin30 = mg
=> N + 8sin30 = 3(9.81)
=> N = 29.43 - 4
=> N = 25.43 Newtons
(where N is the normal force.)

Resolving horizontally: Tcos30 - uN = ma
=> 8cos30 - u(25.43) = 3(0.2)
=> 8cos30 - 0.6 = 25.43u
=> u = 0.2488
(where u is the coefficient of friction.)

Answer 4

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