# Stopping distance using velocity and friction coefficient on an incline plane

• Monic
In summary, the skier will travel 75m up the 10° slope before stopping, given a initial velocity of 20m/s, a coefficient of kinetic friction of 0.10, and a force of gravity acting against her. This was calculated using the equations for distance and acceleration on a slope, taking into account the forces of gravity and friction.
Monic

## Homework Statement

A skier skiing downhill reaches the bottom of a hollow with a velocity of 20m/s, and then coasts up a hill with a 10° slope. If the coefficient of kinetic friction is 0.10, how far up the slope will she travel before she stops?

## Homework Equations

aΔt=v2-v1
d= 1/2(v1 + v2)∆t
d=v1Δt + 1/2aΔt^2
F=ma
μ=Ff/Fn

## The Attempt at a Solution

d=20^2 / 2(9.8)(sin10)(0.1)

I tried to substitute for a in a formuala I found online that worked previously for stopping distance on a horizontal plane.

First you have to take into account the force of gracity slowing her down on the slope as well. Which is Fgrav= - mg sin(10).

Secondly the friction, which is the normal force times the constant of friction. That gives Ffriction = - mg cos (10) * 0.1

The resulting force slowing her down would then be F = -mg ( 0.1cos(10) + sin(10) = ma, implying a = -g(0.1cos(10)+sin(10)).

Now using your top formula we get Δt = (v2-v1)/a = -20/-[g(0.1cos(10)+sin(10))].

Then using the second one gives:

d = 20^2 / 2[g(0.1cos(10)+sin(10))]

Thank you so much! That gets the exact answer in the book (75m) Much appreciated :)

## 1. How is stopping distance affected by velocity on an incline plane?

The higher the velocity, the longer the stopping distance will be. This is because the kinetic energy of the object increases with velocity, and more energy needs to be dissipated to bring it to a stop.

## 2. What role does friction coefficient play in stopping distance on an incline plane?

The friction coefficient determines the amount of resistance or friction between the object and the surface it is traveling on. A higher friction coefficient will result in a shorter stopping distance, as there is more resistance to slow down the object.

## 3. How does the angle of the incline affect stopping distance?

The steeper the incline, the longer the stopping distance will be. This is because a steeper incline will allow the object to gain more speed and momentum, making it harder to stop.

## 4. Is stopping distance always the same on an incline plane?

No, stopping distance will vary depending on the initial velocity, friction coefficient, and angle of the incline. Other factors such as the weight and shape of the object may also play a role.

## 5. Can stopping distance be calculated using a formula?

Yes, stopping distance can be calculated using the formula: d = (v^2)/(2*μ*g*cosθ), where d is the stopping distance, v is the initial velocity, μ is the friction coefficient, g is the acceleration due to gravity, and θ is the angle of the incline.

Replies
5
Views
1K
Replies
33
Views
2K
Replies
18
Views
2K
Replies
2
Views
1K
Replies
5
Views
2K
Replies
7
Views
2K
Replies
4
Views
3K
Replies
4
Views
5K
Replies
1
Views
3K
Replies
2
Views
1K