Distance traveled by a Ball affected by friction after t seconds

• Volt582
In summary, the ball will travel a certain distance after t seconds when it is constantly affected by friction. However, it is complicated to calculate the deceleration, and air resistance should be accounted for as well.
Volt582
Thread moved from the technical math forums to the schoolwork forums
Hi everyone,
i have been trying to find an answer to this problem I have but couldnt find any good answers...
(I dont know much about this stuff, but need a formula for a Project I am currently working on).

So The problem goes as follows:
Assuming we have a ball with a mass of m which is rolling on a flat surface with an initial velocity of v. Lets call the friction coefficiant between the surface and the Ball p. How much distance will the ball have traveled after t seconds when it is constantly affected by friction?

Volt582 said:
Hi everyone,
i have been trying to find an answer to this problem I have but couldnt find any good answers...
(I dont know much about this stuff, but need a formula for a Project I am currently working on).

So The problem goes as follows:
Assuming we have a ball with a mass of m which is rolling on a flat surface with an initial velocity of v. Lets call the friction coefficiant between the surface and the Ball p. How much distance will the ball have traveled after t seconds when it is constantly affected by friction?
A rolling ball is slowly by rolling resistance, rather than friction. In any case, we can assume a constant rate of deceleration. What do you know about motion with constant acceleration?

Volt582
PeroK said:
A rolling ball is slowly by rolling resistance, rather than friction. In any case, we can assume a constant rate of deceleration. What do you know about motion with constant acceleration?
When I have a constant acceleration I should be able to calculate the distance... But how could you calculate the deceleration?

And maybe another question: Do you think that air resistance should be accounted for as well when we are working with a golf ball on a carpet which is approximately traveling with an initial velocity of 6.5 m/s?

Volt582 said:
When I have a constant acceleration I should be able to calculate the distance... But how could you calculate the deceleration?
Rolling resistance is quite complicated. In any case, you are probably going to have to measure things if you want an accurate estimate.
Volt582 said:
And maybe another question: Do you think that air resistance should be accounted for as well when we are working with a golf ball on a carpet which is approximately traveling with an initial velocity of 6.5 m/s?
Probably. But, it would take a bit of work to distinguish the effects of air resistance from rolling resistance. What you will measure directly is a deceleration that involves them both.

Volt582
PeroK said:
Rolling resistance is quite complicated. In any case, you are probably going to have to measure things if you want an accurate estimate.

Probably. But, it would take a bit of work to distinguish the effects of air resistance from rolling resistance. What you will measure directly is a deceleration that involves them both.
mhh ok... Then we will have to perform some more tests. Thanks anyway!

1. How do you calculate the distance traveled by a ball affected by friction after t seconds?

The distance traveled by a ball affected by friction can be calculated using the equations of motion, taking into account the deceleration due to friction. If the initial velocity is $$v_0$$ and the frictional force provides a constant deceleration $$a$$, the distance $$d$$ after time $$t$$ can be found using the formula: $$d = v_0 t - \frac{1}{2} a t^2$$.

2. What factors affect the distance traveled by a ball on a surface with friction?

The distance traveled by a ball on a surface with friction is affected by several factors, including the initial velocity of the ball, the coefficient of friction between the ball and the surface, the mass of the ball, and the duration of time it travels. The coefficient of friction and the mass determine the frictional force, which in turn affects the deceleration of the ball.

3. How does the coefficient of friction influence the distance traveled by the ball?

The coefficient of friction directly influences the deceleration of the ball. A higher coefficient of friction results in a greater frictional force, leading to a higher rate of deceleration and, consequently, a shorter distance traveled by the ball. Conversely, a lower coefficient of friction results in less deceleration and a longer distance traveled.

4. Can the distance traveled by a ball be zero even if it has an initial velocity?

Yes, the distance traveled by a ball can be zero if the time elapsed is zero, meaning the observation is made at the initial moment when the ball starts moving. Additionally, if the frictional force is extremely high, the ball might come to a stop almost immediately, resulting in a very short or negligible distance traveled.

5. How do you experimentally determine the coefficient of friction affecting the ball?

To experimentally determine the coefficient of friction, you can measure the initial velocity of the ball and the distance it travels before coming to a stop. Using the equations of motion, you can calculate the deceleration. The coefficient of friction $$\mu$$ can then be found using the relationship $$f = \mu N$$, where $$f$$ is the frictional force and $$N$$ is the normal force (equal to the weight of the ball if on a horizontal surface). The frictional force can be determined from the deceleration and the mass of the ball.

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