# Coefficient of kinetic friction adding

• A_lilah
In summary, a box of ant aunts and a box of ant uncles slide down an inclined plane while attached by a massless rod parallel to the plane. The angle of incline is 30° and the coefficients of kinetic friction for the two boxes are given. The tension in the rod is calculated to be 0.836722N and the common acceleration of the two masses is found to be 0.7064m/s^2. The mistake in the calculation for part b) was trying to add the coefficients of friction instead of treating it as an extension of part a) and adding the tension force to the force diagram.

## Homework Statement

In the figure below, a box of ant aunts (total mass m1 = 1.15 kg) and a box of ant uncles (total mass m2 = 3.60 kg) slide down an inclined plane while attached by a massless rod parallel to the plane. The angle of incline is θ = 30°. The coefficient of kinetic friction between the aunt box and the incline is µ1 = 0.226. The coefficient of kinetic friction between the uncle box and the incline is µ2 = 0.113.
(a) find the tension in the rod
(b) Compute the common acceleration of the two masses

Fnet = ma

## The Attempt at a Solution

(a) Solved part a and got that the tension was .836722N (which was right)
but I don't think you need that for part b...
(b)
Drew a new FBD for the total system:
W = force down = (mass of m1 + mass of m2)g =46.5975 N
Normal force parallel to the ramp
Frictional force perpendicular to the ramp, going up it

Fnet perpendicular = Normal force - perpendicular component of the weight = N - 46.5975cos(30) = 0 (because it doesn't accelerate in the perpendicular direction)
N = 40.3546

the frictional force = coefficient of friction * normal force

for the coefficient of friction I added the two coefficients given: .113 + .226 = .339 (not sure if this part was right...)

frictional force = 13.6802N up the ramp

so Fnet parallel to the ramp = ma = Parallel weight force - frictional force

Fnet = 46.5975a = 46.5975N * sin(30) - 13.6802

solve for a, which = .7064m/s^2, which wasn't right.

Any help with this second part would be great, thanks!

If you got a) right then you clearly know what you are doing. You've highlighted the problem. You can't add the coefficients of friction. Just treat b) as an extension of a) and add your tension force to one of the force diagrams from a).

oh...

got it :) thanks for your help

## What is the coefficient of kinetic friction and how is it calculated?

The coefficient of kinetic friction, denoted as μk, is a dimensionless quantity that represents the amount of resistance between two surfaces in contact when one is in motion. It is calculated by dividing the force of kinetic friction by the normal force, or μk = Fk/N.

## How is the coefficient of kinetic friction affected by the type of surfaces in contact?

The coefficient of kinetic friction is affected by the type of surfaces in contact as different materials have different levels of roughness and smoothness. Rougher surfaces tend to have higher coefficients of kinetic friction while smoother surfaces have lower coefficients of kinetic friction.

## How does the addition of weight affect the coefficient of kinetic friction?

The addition of weight to an object does not affect the coefficient of kinetic friction. This is because the coefficient of kinetic friction is a property of the surfaces in contact and not of the object itself. However, the weight of an object can affect the normal force, which is used in the calculation of the coefficient of kinetic friction.

## Can the coefficient of kinetic friction be greater than 1?

Yes, the coefficient of kinetic friction can be greater than 1. This occurs when the force of friction is greater than the normal force, resulting in a coefficient of kinetic friction greater than 1. This can happen with very rough surfaces or when there is a lot of force pushing the surfaces together.

## How does the coefficient of kinetic friction affect the motion of an object?

The coefficient of kinetic friction affects the motion of an object by creating a resistance force that opposes the motion of the object. This means that the higher the coefficient of kinetic friction, the more difficult it is for an object to move across a surface. It is an important factor in determining the speed and acceleration of an object in motion.