"A block rests on a rough incline and has coefficients of friction μk= 0.20 and μs= 0.30. If the incline angle increases, at what angle does the block start moving?" ans: 16.7
I tried to write down all the equation, but i find many unknowns! Please anyone help me!
I tried to write down all the equation, but i find many unknowns! Please anyone help me!
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"A block rests on a rough incline and has coefficients of friction μk= 0.20 and μs= 0.30. If the incline angle increases, at what angle does the block start moving?" ans: 16.7
The force which is causing the block to accelerate down the force parallel = mass * g * sin θ
The force which is causing the block to decelerate down the friction force = μ * mass * g * cos θ
Net force = F parallel – F friction = mass * acceleration
mass * g * sin θ – μ * mass * g * cos θ = mass * acceleration
divide both sides by mass
g * sin θ – μ * g * cos θ = acceleration
When acceleration = 0
g * sin θ = μ * g * cos θ
divide both sides by g
sin θ = μ * cos θ
divide both sides by cos θ
sin θ/ cos θ = μ
tan θ = u
friction μk= 0.20 and μs= 0.30. If the incline angle increases, at what angle does the block start moving?" ans: 16.7
To START moving, the block must overcome static friction
tan θ = 0.3
θ = 16.7°
The force which is causing the block to accelerate down the force parallel = mass * g * sin θ
The force which is causing the block to decelerate down the friction force = μ * mass * g * cos θ
Net force = F parallel – F friction = mass * acceleration
mass * g * sin θ – μ * mass * g * cos θ = mass * acceleration
divide both sides by mass
g * sin θ – μ * g * cos θ = acceleration
When acceleration = 0
g * sin θ = μ * g * cos θ
divide both sides by g
sin θ = μ * cos θ
divide both sides by cos θ
sin θ/ cos θ = μ
tan θ = u
friction μk= 0.20 and μs= 0.30. If the incline angle increases, at what angle does the block start moving?" ans: 16.7
To START moving, the block must overcome static friction
tan θ = 0.3
θ = 16.7°
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You need to find out what changes when the block starts moving as opposed to when it is at rest. You already have a hint when you are given the coefficients of friction for static state and kinetic state. Those are your knowns. Also, you know the Normal force is the force of the surface perpendicular to the surface against the block. You need to know the vector of that force because it is not straight up in opposition to gravity, which is straight down. That's where the trigonometry comes in.