Kinetic friction on smooth then rough surface

[rasen58]

Homework Statement

Given a 2.0 kg mass at rest on a horizontal surface at point zero. For 30.0 m, a constant horizontal force of 6 N is applied to the mass.

For the first 15 m, the surface is frictionless. For the second 15 m, there is friction between the surface and the mass.

The 6 N force continues but the mass slows to rest at the end of the 30 m. The coefficient of friction between the surface and the mass is _____.

Homework Equations

F = ma
Work-kinetic energy theorem
F_friction = mu * m * g

The Attempt at a Solution

To solve this, I found the velocity at 15 m by first using F=ma to find that the acceleration for the first 15 m is 3 m/s^2.

Then I used a kinematic equation to find that the velocity at 15 m is sqrt(90).
So then, for the second 15 m, I drew a force diagram and saw that for the mass to decelerate to 0 in the exact same distance as it took to accelerate, then the net force must be the same magnitude but in the reverse direction to slow it down.

So I thought that since it was previously just 6 N to the right, I thought the force of friction would have to be 12 N to the left so that the net force is 6 N to the left.
Force of friction = coeff_fric * m * g

So that means that 12 = coeff_fric * m * g

Solving for coeff_fric, I got 0.6.

But that is apparently wrong since it's supposed to be 0.3.
But the only way to get 0.3 is if Force of friction = 6 N to the left. But I don't see why it should be 6 N instead of 12 N to the left.

 

[Sagar Singh]

total force on the object in rough surface is, [(coffee-of friction)mg-F] coffee of friction = u
by work energy theorem, kinetic energy is lost in doing work against friction,
so F.x=1/2mv^2
F is = [(coffee-of friction)mg-F]
putting values we get
(20u-6)*15=1/2*90*2 ------>15 meters is length of rough surface

20u=12
u=.6
[[[[[[[[correct answer is .6]]]]]]]
if u=.3 then both forces will balance each other so there will be no deceleration
and body will continue
.3 is WRONG answer

 

[NascentOxygen]

@Sagar Singh coffee of friction = coefficient of friction?

I agree with 0.6

 

[Sagar Singh]

@Sagar Singh coffee of friction = coefficient of friction?

I agree with 0.6

haha typing mistake, coefficient of friction
i want to write, (coeff) but it auto corrected to (coffee) to coffee

 

[rasen58]

Thank you everyone! Just wanted to confirm.