# Calculating Coefficient of Kinetic Friction on a Slope Using Newton's Laws

• jmonkey
In summary, you are measuring the co-efficient of kinetic friction between snow and your snowboard. You notice that it takes twice as long to complete the downward portion of it's slide than the upward portion. You use Newton's 2nd law to solve for a and determine that it is negative all the time. This means that the snowboard is accelerating "up" the slope. If (uk) is greater than 1, and the angle x is less than 45 degrees, then (uk)*cos x will be greater than sin x. And then (ad) would have to be positive, which means the snowboard is accelerating "up" the slope...which cannot happen obviously.
jmonkey

## Homework Statement

Note - I have used (uk) as the symbol for co-efficient of kinetic friction (mew k?).

You want to measure (uk) between snow and your snowboard. You measure the angle x the slope makes with the horizontal. You kick your snowboard so it slides up the slope, and then back down. You notice that it takes twice as long to complete the downward portion of it's slide than the upward portion. Determine (uk). The steps to do so are as follows:

1) FBD of snowboard, using variables f and a together with i-hat in the direction up the slop, to represent the friction and acceleration vectors. j-hat is chosen perpendicular to the slope then. What are the signs of f and a on the upward/downward portion of the motion?

2) Use Newton's 2nd law in the i-hat and j-hat directions to solve for a (on the way up and on the way down, denoted (au) and (ad) respectively) in terms of (uk), x and g. Be careful about the sign of f.

...

The question after this point I understand. My problem is coming up with equations for (au) and (ad) that make sense to me. Please help :)

## Homework Equations

NetForce = mass*acceleration
NetForce(i-hat) = mass*accel(i-hat)
NetForce(j-hat) = mass*accel(j-hat)

## The Attempt at a Solution

When I worked this out, I am saying that a is negative all the time (remember (i-hat) is in the direction up the slope), and f is negative on the way up, and positive on the way down. I obtained...

Fnet = Normal*(j-hat) + f(i-hat) - mgsinx(i-hat) - mgcosx(j-hat)
= m*accel = m*a(i-hat)

(i-hat) direction: f-(mgsin x) = ma
(j-hat) direction: N - (mgcos x) = 0

f = (uk) * N = (uk) * mgcos x

I make f negative to solve for (au), and get au = g(-(uk)cos x - sin x). I keep f positive to solve for ad = g( (uk)cos x - sin x). My problem is this. If (uk) happens to be greater than 1, and the angle x is less than 45 degrees, won't (uk)*cos x be greater than sin x. And then (ad) would have to be positive, which means the snowboard is accelerating "up" the slope...which cannot happen obviously. So I assume I have done something wrong. If anything is unclear, please let me know. I realize using (uk) and (ad) creates a lot of clutter. Thanks for your time,

Bump...any suggestions?

Another bump. Sorry to be persistent, but 39 views now, and no one has thoughts (I don't need the problem solved completely, I'm pretty sure my issue is with grasping the variables f and a)? If I'm being too vague/unclear, please let me know.

## 1. What is kinetic friction on a slope?

Kinetic friction on a slope refers to the force that resists the motion of an object as it moves down a slope. It is caused by the interaction between the surface of the slope and the object, and it is dependent on the weight and surface area of the object and the roughness of the surface.

## 2. How is kinetic friction on a slope different from static friction?

Kinetic friction is the force that acts on an object while it is in motion, while static friction is the force that prevents an object from moving when it is at rest. Kinetic friction is typically smaller than static friction, as it only needs to counteract the motion of the object rather than prevent it entirely.

## 3. What factors affect the magnitude of kinetic friction on a slope?

The magnitude of kinetic friction on a slope is affected by the weight and surface area of the object, the roughness of the slope's surface, and the angle of the slope. A heavier object or one with a larger surface area will experience greater friction, as will an object moving down a steeper slope or one with a rougher surface.

## 4. How is the coefficient of kinetic friction related to kinetic friction on a slope?

The coefficient of kinetic friction is a measure of the roughness between two surfaces and is directly related to the magnitude of kinetic friction. A higher coefficient of friction means that there is more resistance to the motion of an object, resulting in a higher kinetic friction force on a slope.

## 5. How can kinetic friction on a slope be reduced?

Kinetic friction on a slope can be reduced by using a smoother surface or reducing the weight and surface area of the object. Additionally, applying a lubricant or reducing the angle of the slope can also decrease the magnitude of kinetic friction. However, it is impossible to completely eliminate kinetic friction on a slope.

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