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bluetriangle
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I'm using a review book to study for physics but I don't understand how this answer was obtained. I got a different answer. When I googled the exact same question, I found a website that got the same answer as me... so is the book wrong? The question is as follows:
1. Homework Statement
A 15 kg crate is moved along a horizontal floor by a warehouse worker who's pulling on it with a rope that makes a 30 degree angle with the horizontal. The tension in the rope is 200 N and the crate slides a distance of 10 m. If the coefficient of kinetic friction between the crate and floor is 0.4, how much work is done by the friction force?
The book uses 10 m/s² for gravity so for the sake of matching answers, I will too.
W = Frcosθ
μ = Ff/Fn
I drew a free body diagram. The only forces acting in the x-direction (direction of the displacement of the crate and therefore what is important to look at when solving for work) are Ftensionx (or Ftx) and Ff.
I know that Ftx = cos30 * 200 = 173.2 N
I know that Ff = μFn = μmg = 0.4*15*10 = 60 (I know Fn = Fg because the crate does not move in the y-direction)
I know that θ = 180 because Ff and the direction of displacement are antiparallel
W = Frcosθ = Ffrcosθ = 60*10*cos180 = -600 J
However, the book says -200 J
Am I doing this wrong?
Thank you for your help
1. Homework Statement
A 15 kg crate is moved along a horizontal floor by a warehouse worker who's pulling on it with a rope that makes a 30 degree angle with the horizontal. The tension in the rope is 200 N and the crate slides a distance of 10 m. If the coefficient of kinetic friction between the crate and floor is 0.4, how much work is done by the friction force?
The book uses 10 m/s² for gravity so for the sake of matching answers, I will too.
Homework Equations
W = Frcosθ
μ = Ff/Fn
The Attempt at a Solution
I drew a free body diagram. The only forces acting in the x-direction (direction of the displacement of the crate and therefore what is important to look at when solving for work) are Ftensionx (or Ftx) and Ff.
I know that Ftx = cos30 * 200 = 173.2 N
I know that Ff = μFn = μmg = 0.4*15*10 = 60 (I know Fn = Fg because the crate does not move in the y-direction)
I know that θ = 180 because Ff and the direction of displacement are antiparallel
W = Frcosθ = Ffrcosθ = 60*10*cos180 = -600 J
However, the book says -200 J
Am I doing this wrong?
Thank you for your help