Calculating Distance of a Ball Rolled on Flat Surface

[Andrew100]

Homework Statement

I want to be able to calculate how far a ball has traveled when rolled along a flat surface at each second.

Lets say the values are 2kg for ball, the force is 100N and co-efficient of friction is 0.2.

Homework Equations

F(n) = -mg
a = f/m

The Attempt at a Solution

I need to find Normal Force (Fn) which is

F(n) = -mg = -(2 kg) * (-9.8 m/s^2) = 19.6 N

I can now use

a = f/m
a = F - (mu)F(n) / m = 100 - ((0.2)(19.6) = 3.92 N / 2 = 1.96 m/s) = 98.04 m/s

So, after 1 second, ball has traveled 96.08 metres (98.04 - 1.96)
2 seconds = 194.12 (98.04 + (98.04 - 1.96))

Is this correct?

 

[kuruman]

I believe that your value for the acceleration is incorrect. Assuming that you have the correct value for the acceleration, use the kinematic equations to find the distance traveled as a function of time.

 

[GRB 080319B]

If the force is horizontal and through the center of the ball, you can use linear motion equations to find distance, but the force of friction in this case is kinetic, since the ball can't roll if no torque is applied. For this case, net force is applied force minus force of kinetic friction. If the force is not dead center, then you have to determine the angular motion equations, starting with net torque is equal to applied torque minus torque due to static friction, which is equal to rotational inertia of ball times it's angular acceleration. Solve for angular acceleration, and then derive the angular motion equations. Then, you can determine linear speed from angular speed by v = omega * R, where R is radius of ball, if the applied force is constant and there is no slipping.

 

[Torquescrew]

Are we married to the idea of kinetic friction, though?
Like... a car's tires rely on static friction to propel itself forward, to come to a stop (when using anti-lock brakes), to turn (etc) all without slipping or skidding. Kinetic friction comes from sliding, right? But the ball is rolling. Not sliding.
Not trying to to stick my nose in business that isn't mine or anything like that.
Just seems odd. After all, if the ball was skidding as it rolled, we couldn't actually know how far it would roll. It would get less traction than it should. <-equates to not going as far as it should.

 

[Andrew100]

Once I have the acceleration, what formula do I need to use to calculate the decreasing velocity?
How can I find out how far the ball will travel in total if I have accelaration but not time?

Hope someone can help

 

[kuruman]

What Torquescrew is saying is, ideally, correct. One cannot find how far your rolling ball travels from the information you have given. However, if you have a value for the acceleration, then you must use the kinematic equations to find the distance. You can find the kinematic equations at

https://www.physicsforums.com/showpost.php?p=905663&postcount=2

 

[Andrew100]

Still confused but here is my working.
Looking at the link to the kinematic formulas I can see that I need to use

x = x0 + (1/2)at2, I assume Vot does not apply if I do not want to calculate how high the ball is hit.

So let's say the acceleration was 25 m/s.

x = 25 + (0.5)*25 * t2 (Initial Velocity x0 = Acceleration?)
x = 25 + (0.5)*25 * t2
x = 25 + 12.5 * t2
x = 25 + 12.5 * (25*10)
x = 3125 meters

So after 10 Seconds, the ball has traveled 3125 meters?
But how do I minus the friction?

I still do not understand how I get the distance though?
All the kinematic equations want a value for t which I do not know?

 

[denverdoc]

assume that it is not rolling--lets say it is a block instead of a ball to remove any confusion.

You did much of the work in your initial post: the a=(100-2*9.8*0.2)/2
You can use x=1/2at^2 for say 5 and 6 seconds and subtract the first value from the second to get the distance traveled during second 5.

Alternatively, since the acceleration is constant,

the velocity at 5 seconds is just 5*a
the velocity at 6 seconds is 6*a.
the average velocity is 5.5a and the distance traveled in that second is 5.5a*1