Physics help please?

Question

ok, a 90kg clock initially at rest on a horizontal floor requires a 650 N horizontal force to set it in motion. After the clock is in motion, a horizontal force of 560 N keeps it moving with a constant speed. find mu s and mu k between the clock and the floor.

Any help at all is appreciated. thanks!

Answer 1

1) Draw a Force Diagram:

(I'm just going to list the forces b/c i can't really draw them)

(x) + Force Push (Fp)
(x) - Force Friction (Ff)
(y) + Force Normal (Fn)
(y) - Mass*Gravity (mg)

2) Break your forces up into their x and y equations

x:
Fp - Ff = ma
a = 0 (b/c it is @ a constant velocity)
Fp - Ff = -
Fp = Ff

y:
Fn - mg = ma
a =0 (b/c the clock isn't moving up or down)
Fn - mg = 0
Fn = mg

3) Solve for Friction
Ff = (mu)Fn
Ff = (mu)mg

4) Plug Ff back into your x equation
Fp = (mu)mg

5) Setup to solve for mu s and mu k
Fp = (mu)mg
(Fp / mg) = (mu)

6) Plug in your values and solve for mu s and mu k
(650 / (90 * 9.8) = (mu s)
(560 / (80 * 9.8) = (mu k)

I came up with:
mu s = .73696
mu k = .6349

Answer 2

Okay, so all you need to remember is that the coefficient of friction, is simply the dimensionless quantity that relates the normal force to the force of friction.

In other words... F_static = mu_static * F_normal... and
F_kinetic = mu_kinetic * F_normal.

So, we have to define the quantity "F_normal." Let us think back to Newton's second law, F=ma. In the case of the clock, the "F_normal" is simply F=ma for the clock, where "a" is gravity! Remember that gravity is an acceleration, and since the direction of gravity is 90-degrees to the plane of the floor, it is also the normal force.

Now we have F_normal = 90*9.8. That is approximately 900Newtons, right? (It's technically 882 Newtons).

Let's solve for the coefficient of STATIC friction.

We take F_friction = mu_s * F_normal. Divide F_friction by F_normal and that is mu_s. Aka... mu_s = 650/882.

Let's solve for the coefficient of KINETIC friction.

Take F_friction = mu_s * F_normal. Divide F_friction by F_normal and that is mu_k. Aka... mu_k = 560/882.

Plug those values into your calculator and there you go!

Answer 3

Static friction force = µs*normal force. In this case, normal force = m*g, so

µs = 650N / 90*g (static)

When the object moves at constant velocity, the driving force = frictional force.

µk = 560N/ 90*g (sliding)