Solve Friction Problem: Find Force w/ Coefficient 0.3

[-Physician]

Homework Statement

A ball horizontally with an initial velocity of 5m/s,and the ball stops at 8.0m. Find the force of friction if the coefficient is 0.3.

Homework Equations

$F_net=ma$
$v^2=v_0^2 2ax$
$a=\frac{v_1^2 - v_0^2}{2ax}$
$f=μN$
$N=mg$ (In this case the normal force is equal to weight.)

The Attempt at a Solution

$a=\frac{v_1^2 - v_0^2}{2ax}=\frac{-25\frac{m^2}{s^2}}{16m}=-1.56\frac{m}{s^2}$
$F_net=ma$
$f=ma$
$μN=ma$
$μmg=ma$
$μg=a$(Masses cancel out because the mass doesn't matter on rotary bodies.
$μg=a$ I'm stuck here, how can I find the friction?!

 

[Liquidxlax]

how do you do this question without mass?

 

[-Physician]

In rolling objects/bodies the mass doesn't matter.

 

[Shootertrex]

how do you do this question without mass?

I agree. Since frictional force in this case depends on mg, it would be impossible to calculate it without mass.

The units for force are kg*m/s², so it would be unreasonable to ask one to calculate force without a mass.

As a side note, I was able to calculate two different accelerations using the formulas provided. Using v_{f}²=2ad+v_{i}² I got the same acceleration that you had: -1.56.
Using the second equation using acceleration, μg=a, I got 2.94.

This fact alone makes me wonder if it is even possible, but it also implies that there is another force that we are not seeing that is affecting the motion of the ball.

In rolling objects/bodies the mass doesn't matter.

If you are talking about all rolling objects/bodies, then I am almost certain that you are wrong. The moment of inertia for objects is very much subject to mass and mass distribution.

Now back to the problem at hand. I can see the acceleration being independent, but not the force. I have actually been searching around the internet trying to find equations that would help solve this, but I was not successful. Though I did find this, courtesy of Wikipedia:

F_{r}=C_{rr}N

where F_r is rolling resistance, C_rr is the rolling resistance coefficient, and N is normal force. And again, the force is subject to the mass. Though I do not think this equation would be of use in this situation given the provided information anyway.

If possible, can you, or anyone, provide a link to a site that shows that friction in this case would be independent to mass? I would much like to correct myself if I am wrong.

 

[-Physician]

I saw a video on youtube with this task, but the task was to find the coefficient, and I tried to give the coefficient and find friction, but I see it's impossible if we don't give the mass of the body. Video link:

 

[Shootertrex]

I saw a video on youtube with this task, but the task was to find the coefficient, and I tried to give the coefficient and find friction, but I see it's impossible if we don't give the mass of the body. Video link:

Thank you for the link. Yeah, the video showed that the coefficient of friction is independent of mass not the force as we already know.

If the answer to this problem is provided, see if it has m within the answer. If it does, then you are set. If it doesn't, well, all I can say is that we have a long way to go.