# Finding the speed with kinetic friction

• dominatesean
In summary, the conversation discusses a scenario where you and your friend are putting new shingles on a roof. Your friend asks for a box of nails, which you decide to push down the roof to him instead of carrying it. The problem is to determine the velocity at which you should push the box so that it gently comes to rest at the edge of the roof. The solution involves finding the normal force and kinetic friction, and using kinematic equations to calculate the acceleration and final velocity. The final answer is determined to be 9.3 m/s.
dominatesean

## Homework Statement

You and your friend Peter are putting new shingles on a roof pitched at 20degrees . You're sitting on the very top of the roof when Peter, who is at the edge of the roof directly below you, 5.4 m away, asks you for the box of nails. Rather than carry the 2.1 kg box of nails down to Peter, you decide to give the box a push and have it slide down to him.

If the coefficient of kinetic friction between the box and the roof is 0.51, with what speed should you push the box to have it gently come to rest right at the edge of the roof?

## Homework Equations

normal force up y-axis
mg down y-axis
angle left of -y
friction positive x
not 100% sure if these are right

n-mg*cos O=may
fk+mg(sin O)=max
vf=vi+at
xf=xi+vi*t+.5at^2

## The Attempt at a Solution

first get normal force which solve for 1st equ.
n=2.1(9.8)cos20=19.34
then find kinetic friction
19.34*.51=9.86
put into next equation
9.86+2.1(9.8)sin20=2.1*a
a=8.047

plug into kinematic equ.
5.4=0+0*t+.5(8.047)t^2
t=1.15
vf=8.047*1.15
vf=9.3

obviously not right cause I am not sure about the free-body diagram any help would be fantastic.

What will the acceleration (deceleration) be?

It will be the gravity component down the slope less the frictional slowing = g*sinθ - μ*g*cosθ = a

Since the final velocity is 0, now you can simply use the V2 = 2*a*x

thank you my friend...that was much easier then I thought it was.

## 1. How do you calculate the speed with kinetic friction?

The speed with kinetic friction can be calculated using the formula: v = √(2μmg)/m, where μ is the coefficient of kinetic friction, m is the mass of the object, and g is the acceleration due to gravity.

## 2. What is the difference between static friction and kinetic friction?

Static friction is the force that prevents an object from moving while it is at rest, while kinetic friction is the force that opposes the motion of an object that is already in motion.

## 3. How does the coefficient of kinetic friction affect the speed of an object?

The coefficient of kinetic friction is directly proportional to the speed of an object. This means that as the coefficient of kinetic friction increases, the speed of the object decreases.

## 4. Can the speed with kinetic friction be greater than the initial speed of the object?

No, the speed with kinetic friction can never be greater than the initial speed of the object. This is because kinetic friction always acts in the opposite direction of the object's motion, causing it to slow down.

## 5. What are some factors that can affect the speed with kinetic friction?

The speed with kinetic friction can be affected by various factors such as the surface roughness of the object and the surface it is moving on, the mass of the object, and the coefficient of kinetic friction between the two surfaces.

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