Speed of an object sliding down

[AlexanderIV]

Homework Statement

An object of mass m=2 kg slides down on a track from a height of h = 10 m. The track is frictionless except the horizontal range between the points A and B. The friction force is constant between A and B. What is the speed of the object at point B if the magnitude of the friction force between A and B is f = 10 N (take g = 10 m/s2) .

Homework Equations

F = m (dv / dt)
KE = 1/2 mv^2

The Attempt at a Solution

The potential energy while sliding down would be U=mgh=2x10x10=200 J[/B]
I have no idea what to do after this point.

 

[haruspex]

Relevant equations

What equation connects work and force?

 

[AlexanderIV]

What equation connects work and force?

W = Fdcosθ

 

[haruspex]

W = Fdcosθ

Can you apply that to the strip AB?

 

[AlexanderIV]

If I apply it would be W = Fdcosθ = (mgsinθ)x10xcos0= (2x10xsin0)x10x1=0 but that does not make sense to me.

 

[haruspex]

If I apply it would be W = Fdcosθ = (mgsinθ)x10xcos0= (2x10xsin0)x10x1=0 but that does not make sense to me.

What force affects the speed?

 

[AlexanderIV]

The gravitational force affects the speed. Then it should be W = Fdcosθ = (mg)dcosθ = (2x10)x10x1 = 200 J?

 

[haruspex]

The gravitational force affects the speed.

No, I mean along the strip AB.

 

[AlexanderIV]

No, I mean along the strip AB.

The friction force.

 

[haruspex]

The friction force.

So write the energy equation in relation to that.

 

[AlexanderIV]

W = (mgsinθ - kmg)dcosθ = (2x10x0 - kx2x10)x10x1 = (0-20k)x10 = -200k J ?

 

[haruspex]

W = (mgsinθ - kmg)dcosθ = (2x10x0 - kx2x10)x10x1 = (0-20k)x10 = -200k J ?

I assume k represents the coefficient of kinetic friction, but you are not given that. You don't need it because you are given the actual frictional force.

 

[AlexanderIV]

Then it should be -100 J but I don't know how I could relate that to the speed.

 

[haruspex]

Then it should be -100 J but I don't know how I could relate that to the speed.

You don't know how a change in energy relates to a change in speed? You quoted an expression for KE.

 

[AlexanderIV]

-100 = 1/2mv^2 => -100=v^2 => -100=v^2

But this is not possible, is it?

 

[haruspex]

-100 = 1/2mv^2 => -100=v^2 => -100=v^2

But this is not possible, is it?

It started with some energy. The work done by friction is only a deduction from that.

 

[AlexanderIV]

It started with potential energy, so W = Fdcosθ = (mgh - f)dcosθ = (200 - 10)10 = 190 x 10 = 1900 J?

 

[haruspex]

mgh - f

That makes no sense. You are subtracting a force from an energy term.
What energy did it gain by descending, and what does it lose to friction?