# An object with a mass of #8 kg# is on a plane with an incline of # - pi/3 #. If it takes #15 N# to start pushing the object down the plane and #12 N# to keep pushing it, what are the coefficients of static and kinetic friction?

If angle is

#mu_s = 0.798#

#mu_k = 0.754#

See explanation regarding angle.

We're asked to find the coefficient of static friction

We'll call the positive *up* the incline (the direction of

There is no net vertical force, so we'll look at the horizontal forces (we WILL use the normal force magnitude

We're given that the object's mass is

Since the angle is

#-(pi)/3# , this would be the angle goingdownthe incline (the topmost angle in the image above). Therefore, the actual angle ofinclinationis

#pi/2 - (pi)/3 = ul((pi)/6#

The formula for the coefficient of static friction

#f_s <= mu_sn#

Since the object in this problem "breaks loose" and the static friction eventually gives way, this equation is simply

#color(green)(ul(f_s = mu_sn#

Since the two vertical quantities

#n = mgcostheta = (8color(white)(l)"kg")(9.81color(white)(l)"m/s"^2)cos(pi/6) = color(orange)(ul(68.0color(white)(l)"N"#

Since

#color(green)(f_s) = mgsintheta + 15# #"N"#

#= (8color(white)(l)"kg")(9.81color(white)(l)"m/s"^2)sin(pi/6) + 15color(white)(l)"N" = color(green)(54.2color(white)(l)"N"#

The coefficient of static friction is thus

#mu_s = (f_s)/n = (color(green)(54.2)cancel(color(green)("N")))/(color(orange)(68.0)cancel(color(orange)("N"))) = color(red)(ulbar(|stackrel(" ")(" " 0.798" ")|#

The coefficient of kinetic friction

#color(purple)(ul(f_k = mu_kn#

It takes

#color(purple)(f_k) = mgsintheta + 8# #"N"#

#= 39.2color(white)(l)"N" + 12# #"N"# #= color(purple)(51.2color(white)(l)"N"#

The coefficient of kinetic friction is thus

#mu_k = (f_k)/n = (color(purple)(51.2)cancel(color(purple)("N")))/(color(orange)(68.0)cancel(color(orange)("N"))) = color(blue)(ulbar(|stackrel(" ")(" " 0.754" ")|#

By signing up, you agree to our Terms of Service and Privacy Policy

To calculate the coefficients of static and kinetic friction, we need to use the equations involving force and friction on an inclined plane. The force required to start pushing the object down the plane is equal to the product of the coefficient of static friction and the normal force exerted on the object. Similarly, the force required to keep pushing the object once it's in motion is equal to the product of the coefficient of kinetic friction and the normal force.

Given that it takes 15 N to start pushing the object down the plane and 12 N to keep pushing it, and the mass of the object is 8 kg, we can calculate the normal force using the formula:

Normal force (N) = mass (kg) * gravitational acceleration (m/s^2)

Then, we can use the force equations involving friction to solve for the coefficients of static and kinetic friction.

First, we solve for the normal force:

Normal force = 8 kg * 9.8 m/s^2 = 78.4 N

To find the coefficient of static friction:

15 N = coefficient of static friction * 78.4 N

Coefficient of static friction = 15 N / 78.4 N

To find the coefficient of kinetic friction:

12 N = coefficient of kinetic friction * 78.4 N

Coefficient of kinetic friction = 12 N / 78.4 N

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < 3 N , 2 N># and the second is #F_2 = < 7 N, 6 N>#. What is the object's rate and direction of acceleration?
- A box with an initial speed of #8 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #1/2 # and an incline of #(3 pi )/8 #. How far along the ramp will the box go?
- If the length of a #27 cm# spring increases to #65 cm# when a #4 kg# weight is hanging from it, what is the spring's constant?
- An object with a mass of # 8 kg# is on a ramp at an incline of #pi/8 #. If the object is being pushed up the ramp with a force of # 7 N#, what is the minimum coefficient of static friction needed for the object to remain put?
- A truck pulls boxes up an incline plane. The truck can exert a maximum force of #5,600 N#. If the plane's incline is #(2 pi )/3 # and the coefficient of friction is #8/5 #, what is the maximum mass that can be pulled up at one time?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7