# [Forces/Kinematics] How far will skateboarder go?

• brbrett
In summary, the conversation discusses how to approach a question about a skateboarder coasting on flat, rough ground with an initial velocity of 7.5 m/s. The question asks how far the skateboarder will go before stopping, using kinematics and forces in combination. The conversation also touches on the use of symbols and the mass problem, as well as the importance of considering rolling resistance instead of just friction. Ultimately, the solution is found to be 22.95 meters by solving for the distance using one of the kinematic equations.
brbrett

## Homework Statement

Suppose a skateboarder is coasting initially at 7.5 m/s to the right across flat, rough ground (coefficient of friction = 0.125). How far will the skateboarder go before stopping. (Kinematics and forces will be used in combination)

v2=v1+at
v=d/t
d=v0t+(1/2)at2
F=ma

## The Attempt at a Solution

I'm not certain how to approach the question. The question doesn't state what the mass is, nor any applied force apart from the initial velocity. I know that the final velocity is 0.

You don't need the mass, work symbolically (ie don't plug any numbers in until the end) and it'll all work out.
Does this formula ring any bells?
Ff = μN

I tried doing the problem symbolically, but I've run into the mass problem again. Here is my work:
Ff = μN
a=Ff/m
v22=v02+2(Ff /m)d
This time I have figured out what "a" is, and I only need to know the inside parts of it (m and Ff)

brbrett said:
I tried doing the problem symbolically, but I've run into the mass problem again. Here is my work:
Ff = μN
a=Ff/m
v22=v02+2(Ff /m)d
This time I have figured out what "a" is, and I only need to know the inside parts of it (m and Ff)

Getting there.
What is 'N'? It's definition can be used to eliminate m.

Normal force is the reaction force to gravity.
Can I do this then?
g is gravity
Ffr= μ(gm)
a= [μ(gm)]/m
a= μg

that would cancel out the mass and leave me with 9.8

brbrett said:
Normal force is the reaction force to gravity.
Can I do this then?
g is gravity
Ffr= μ(gm)
a= [μ(gm)]/m
a= μg
Your math is right but I'm not sure what you mean by this:
that would cancel out the mass and leave me with 9.8
'g' is 9.81 m/s2 but 'a' won't have that value.

You'll also have to be aware of the directions of v and a and get their signs right to get the right answer.

err, that was an error from before I altered my math. a is actually μg, so gravity times that coefficient of friction will give me the acceleration, which will be negative since we are talking about slowing an object down.

brbrett said:
err, that was an error from before I altered my math. a is actually μg, so gravity times that coefficient of friction will give me the acceleration, which will be negative since we are talking about slowing an object down.
Good work. You're pretty much there. Just solve for d then plug and chug.

Thanks for the help.
I got 22.95 meters as my answer when I used one of the kinematic equations.

brbrett said:
Thanks for the help.
I got 22.95 meters as my answer when I used one of the kinematic equations.
I agree with that answer, but I would like to point out a serious flaw in the wording of the question.
A skateboard has wheels. Wheels roll. In rolling contact, friction is static, and static friction does no work. No matter how high the coefficient of friction, it won't slow the skateboard at all.
What slows the skateboard is rolling resistance. This consists of absorbency in the springiness of the ground and wheels, and torsional friction at the wheel axles.

Unfortunately the problem is taken from an introductory physics course, where we have yet to learn anything more about friction and how it works. My teacher often makes questions with serious flaws like this though, especially with work/energy.

Thanks! I'll definitely take a look at it.

## 1. What is the initial velocity of the skateboarder?

The initial velocity of the skateboarder depends on a few factors, such as the force of the push-off and the slope of the surface they are skating on. Typically, it can range from 0-10 miles per hour.

## 2. How does the mass of the skateboarder affect their distance?

The mass of the skateboarder does not directly affect the distance they will travel. However, a heavier skateboarder may have a harder time achieving a higher initial velocity and may experience more resistance from air resistance and friction, leading to a shorter distance traveled.

## 3. What role do forces play in determining the distance a skateboarder will go?

Forces, such as gravity and friction, play a significant role in determining the distance a skateboarder will go. Gravity pulls the skateboarder downward, while friction from the surface and air resistance act as opposing forces to slow them down. These forces can affect the skateboarder's speed and trajectory, ultimately determining their distance.

## 4. Is there a maximum distance a skateboarder can go?

The maximum distance a skateboarder can go is influenced by various factors, such as the initial velocity, the slope of the surface, and the presence of obstacles. In a perfect scenario with no external forces, a skateboarder could theoretically travel an infinite distance. However, in real-world situations, other factors often limit the maximum distance they can go.

## 5. How can we calculate the distance a skateboarder will go?

The distance a skateboarder will go can be calculated using the equation d = v2 / 2a, where d is the distance, v is the initial velocity, and a is the acceleration. This equation assumes constant acceleration, which is not always the case for a skateboarder. Other factors, such as air resistance and changes in surface slope, may also need to be taken into account for a more accurate calculation.

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