# Does mass impact speed on a ramp?

• UseAsDirected
In summary, the concept of mass having an impact on an inclined plane can be a confusing topic to teach. While mass does not have an impact on an inclined plane according to mathematical equations, students may argue that heavier objects can travel farther or faster due to factors such as air resistance or the moment of inertia. However, these arguments can be disproven through the use of first principles and the understanding that friction is proportional to mass. Ultimately, when considering identical objects with different masses, they should travel at the same speed and cross the finish line at the same time on an inclined plane.
UseAsDirected
Mentors Note: Posts from a duplicate thread have been merged into this one.

Hello, please explain the following in detail. I am a learning assistant (LA) at a major university but am stuck explaining a concept to my students.

Does mass have an impact on an inclined plane? A cart with wheels or a block of wood sliding down? I say, no. And, I can mathematically show this. However, my students showed me a Java applet in which a mass is put into a toy truck, and, upon its release off of a ramp, the travels farther! Is this true?

When I substantiate my claim, I continually get the masses to cancel.

acceleration = g * (-mu_k * cos(theta) + sin(theta) ). (equation 1)
simple model, I get

mu_k = a/g (equation 2)

Where mu_k is the coefficient of kinetic friction.

Mass never appears.

The students said that on Olympic bobsled on Wikipedia, the claim is that heavier sledders sleigh down faster. On YouTube videos, heavier skate boarders skate down faster.

I keep claiming that, using conservation of energy,

v = sqrt(2gh) (equation 3).

Am I right or are they right? I tutor an entire class of university students and I am angry at myself for getting entangled in something I should know.

Thank you.

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UseAsDirected said:
Does mass have an impact on an inclined plane?
If you consider air resistance, then yes. Just like during falling through the atmosphere.

UseAsDirected said:
travels farther
"Farther" I can see. If you meant "faster," take a look at the moment of inertia of the wheels on the cart/truck. It should be insignificant, but depending on magnitude, might have an effect.
UseAsDirected said:
Olympic bobsled on Wikipedia
Sounds like "Cool Runnings" and John Candy are tough to argue with in students' minds. Coefficient of friction for the two different sled masses on same runners ----- tough to say constant, and tough to say what might affect it. Film thickness if we subscribe to the change in m.p. temperature with pressure idea, and any number of folklore ideas if we listen to sportscasters, script writers, or real competitors.

Help any?

A.T. said:
If you consider air resistance, then yes. Just like during falling through the atmosphere.

What is the skateboarders and bobsleigh practitioners are shaped exactly the same? What is instead I roll to identical balls of different masses?

Bystander said:
"Farther" I can see. If you meant "faster," take a look at the moment of inertia of the wheels on the cart/truck. It should be insignificant, but depending on magnitude, might have an effect.

Sounds like "Cool Runnings" and John Candy are tough to argue with in students' minds. Coefficient of friction for the two different sled masses on same runners ----- tough to say constant, and tough to say what might affect it. Film thickness if we subscribe to the change in m.p. temperature with pressure idea, and any number of folklore ideas if we listen to sportscasters, script writers, or real competitors.

Help any?

Hello! Thank you for response. Oh, actually, I think I am mixing farther and faster.

The heavier travels farther, but not faster, is that right? It does not travel faster is my claim. I see your point about the misconceptions of sports casters. If you go onto Wikipedia "Bobsleigh" the Olympic section immediately posts that weight matters.

So, is it physically correct to say that, given the same roughness index of surface area of two people on identical sleds, they will sled down at the same speed and cross the finish line at the same time?

UseAsDirected said:
What is the skateboarders and bobsleigh practitioners are shaped exactly the same?
Same shape & size makes the more massive object faster.

UseAsDirected said:
What is instead I roll to identical balls of different masses?
Rolling makes the speed also dependent in the moment of inertia (mass distribution).

A.T. said:
Same shape & size makes the more massive object faster.

Rolling makes the speed also dependent in the moment of inertia (mass distribution).
Yes, yes, I see. Now, two identical block of different masses? They must travel at same speed and cross line at same time, correct?

UseAsDirected said:
Yes, yes, I see. Now, two identical block of different masses? They must travel at same speed and cross line at same time, correct?

There was some lame response I saw on a forum by a student on a national laboratory and, the writer said that heavier objects on ramps can overcome friction whereas lighter ones cannot. I think that is categorically wrong. Friction is proportional to mass and there is no way to "overcome" friction. Is that right?

Bystander said:
"Farther" I can see. If you meant "faster," take a look at the moment of inertia of the wheels on the cart/truck. It should be insignificant, but depending on magnitude, might have an effect.

Sounds like "Cool Runnings" and John Candy are tough to argue with in students' minds. Coefficient of friction for the two different sled masses on same runners ----- tough to say constant, and tough to say what might affect it. Film thickness if we subscribe to the change in m.p. temperature with pressure idea, and any number of folklore ideas if we listen to sportscasters, script writers, or real competitors.

Help any?

Sorry to inundate you with this. So, a student of mine claims that when his group does the blocks-on-ramp experiment, the heavier block slides off first (i.e., at a lower angle). I said this cannot be possible. This goes against everything I know. They taped heavy washers onto one block but not the other. This cannot possibly be true, can it? When I derive the equation from first principles, the masses always cancel!

I can only see this situation: heavy block travels farther because of the effects of inertia. But, does not travel faster. And, does not have a lower angle-of-slip.

UseAsDirected said:
cross the finish line at the same time?
Same mass, they should. The coefficient of friction on ice being constant no matter what the load --- I've listened to too many hockey games and no longer can convince myself I've got a clue. I'm reasonably certain the "pressure melting" (it's only a few hundredths of a degree for loads on ice skates) can't be it, but at the same time, ice skates and bobsled runners are "hollow ground" and the loading area and pressure may be variable --- that's actually your out on that item, come to think of it.

As "far" as the cart with two different masses is concerned, the heavier cart will furnish more torque to accelerate the rotational motion of the wheels, and does accelerate more rapidly. As I said, most carts I've seen have very low mass wooden wheels, and it should be a miniscule difference.

Bystander said:
Same mass, they should. The coefficient of friction on ice being constant no matter what the load --- I've listened to too many hockey games and no longer can convince myself I've got a clue. I'm reasonably certain the "pressure melting" (it's only a few hundredths of a degree for loads on ice skates) can't be it, but at the same time, ice skates and bobsled runners are "hollow ground" and the loading area and pressure may be variable --- that's actually your out on that item, come to think of it.

As "far" as the cart with two different masses is concerned, the heavier cart will furnish more torque to accelerate the rotational motion of the wheels, and does accelerate more rapidly. As I said, most carts I've seen have very low mass wooden wheels, and it should be a miniscule difference.
Right, yes, thank you.

UseAsDirected said:
Now, two identical block of different masses? They must travel at same speed and cross line at same time, correct?
Not if air resistance is considered, as I already said.

UseAsDirected said:
Friction is proportional to mass
That is the most simple friction model. Not sure if it's still accurate on real ice, for bobsleds and skaters.

Blocks on ramp: this is static friction? Tip them up and see at what angle they start to slide? Taping weights on top of the block and tipping is NOT generally going to be loading the contact area between the block and ramp uniformly, at which point, I don't want to be the guy trying to integrate normal force over contact area to say what's going to happen. For a lab I'd want a block with a hole drilled through the center of mass from one side (not end) to the other that I could insert a close fitting brass, iron, lead weight into for such an experiment.

Bystander said:
Blocks on ramp: this is static friction? Tip them up and see at what angle they start to slide? Taping weights on top of the block and tipping is NOT generally going to be loading the contact area between the block and ramp uniformly, at which point, I don't want to be the guy trying to integrate normal force over contact area to say what's going to happen. For a lab I'd want a block with a hole drilled through the center of mass from one side (not end) to the other that I could insert a close fitting brass, iron, lead weight into for such an experiment.

Yes, this is a static friction tipping experiment. Students claim heavier block slips at a lower angle. I will discuss tomorrow with the laboratory manager about your second recommendation, then replicate the experiment myself. Thanks. Seems like reality is not so simple as theory.

Indeed, Google suggests that it's not "pressure causing ice to melt" that makes it slippery...

http://www.exploratorium.com/hockey/ice2.html

In the past, scientists believed that either pressure or friction melted the ice, creating a water lubricant that allows skates and pucks to slide. Berkeley chemist Michel van Hove, a colleague of Somorjai's, has done calculations which show that skates and pucks do not generate enough pressure to instantly liquefy ice. Somorjai has discovered that ice has a "quasi-fluid layer" that coats the surface of ice and makes it slippery. Even ice that is 200 degrees below zero Fahrenheit (-129 Celcius) or more still has this layer.

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UseAsDirected said:
Sorry to inundate you with this. So, a student of mine claims that when his group does the blocks-on-ramp experiment, the heavier block slides off first (i.e., at a lower angle). I said this cannot be possible. This goes against everything I know. They taped heavy washers onto one block but not the other. This cannot possibly be true, can it? When I derive the equation from first principles, the masses always cancel!

The frictional force equation Ff = μFN, with constant μ, is only an approximation for a limited range of FN. For example, if the mass is heavy enough to "dig into" the surface it is resting on, that will make a difference. Also, in a typical student lab setup, it's hard to make the surface conditions exactly reproducible from one trial to the next.

jtbell said:
The frictional force equation Ff = μFN, with constant μ, is only an approximation for a limited range of FN. For example, if the mass is heavy enough to "dig into" the surface it is resting on, that will make a difference.
Right, but his students reported the heavier block as moving faster, which could be an effect air resistance. The same air resistance slows a light object more than a heavy object.

I guess we must remember that this was a java applet not a real world experiment. Quite possible that whoever wrote the code got it wrong.

Any chance of a URL?

Regarding quality of ice, coefficients of friction, myths and folklore, the following link may be interesting.
http://www.covers.com/articles/articles.aspx?theArt=169900
Last winter olympics, there was a fair amount of time devoted to details of surface preparation for curling, including temperature, "pebbling" of the surface, and other esoteric details. None of this is reference quality data, but may serve to illustrate the scope of the problems to be dealt with when discussing coefficient of friction and ice surfaces.

Heavier sledders are less affected by air resistance, since the force of gravity scales with their mass, while the force of drag scales with their cross sectional area. Generally mass increases faster than area, so at larger scales, gravity wins out. (For similar shapes, area scales as length^2, and mass scales as length^3. Generally, viscous drag becomes less important for larger objects. Research "Reynolds number" for related info.)

Snow is not quite a fluid, but probably takes on some of its characteristics at high relative velocity.

Bystander said:
Regarding quality of ice, coefficients of friction, myths and folklore, the following link may be interesting.
http://www.covers.com/articles/articles.aspx?theArt=169900
Last winter olympics, there was a fair amount of time devoted to details of surface preparation for curling, including temperature, "pebbling" of the surface, and other esoteric details. None of this is reference quality data, but may serve to illustrate the scope of the problems to be dealt with when discussing coefficient of friction and ice surfaces.

Here two videos on this topic:

Khashishi said:
Heavier sledders are less affected by air resistance, since the force of gravity scales with their mass, while the force of drag scales with their cross sectional area.
Exactly.

Khashishi said:
Heavier sledders are less affected by air resistance, since the force of gravity scales with their mass, while the force of drag scales with their cross sectional area. Generally mass increases faster than area, so at larger scales, gravity wins out. (For similar shapes, area scales as length^2, and mass scales as length^3. Generally, viscous drag becomes less important for larger objects. Research "Reynolds number" for related info.)

Snow is not quite a fluid, but probably takes on some of its characteristics at high relative velocity.

Hello Khashishi. Will a heavier bobsled come down faster than a lighter one even though both sleds are exactly the same?

A.T. said:
Here two videos on this topic:

Thank you. I watched the curling video and I found a contradiction (or, I am stupid, likely). The curling block, if it has a flat bottom, has more contact area and runs slower than if it has less surface area. I have done experiments that show that contact area does not affection friction. In our physics laboratory, we take large, heavy rectangular blocks and drag them across tables attached to spring cables. No matter on which face we put the blocks (large side, medium side, small side), the force of friction on the spring scale is the same. I confirmed this with laboratory manager. The only difference is that more pressure is on the small side, wearing it out sooner. The above contradicts.

UseAsDirected said:
Will a heavier bobsled come down faster than a lighter one even though both sleds are exactly the same?
If shape and size are the same, the heavier one will be faster based on aerodynamics. But if you make it too heavy it will plow into the ice too much and become slower again.

UseAsDirected said:
In our physics laboratory, we take large, heavy rectangular blocks and drag them across tables ...
The video is about ice, not tables.

A.T. said:
The video is about ice, not tables.

Why? Because a thin condensed matter film forms on ice, and that variable makes the situation different?

I've only read the introduction but perhaps it helps explain the problem with modelling friction of different types..

http://aspe.net/publications/Spring_2010/Spr10Ab/1010AlBender.pdf

Friction modeling has been steadily gaining in interest over the last few decades. However, owing to the complexity of the friction phenomenon, no comprehensive, practicable friction model that shows all of the experimentally observed aspects of friction force dynamics in one formulation is available. Most available friction models are, in essence, empirical, that is, based on limited observations and interpretations. In this sense, the resulting models are valid only for the specific scope of test conditions, such as the level and type of excitation, used to obtain the data.

## 1. Does mass affect the speed of an object on a ramp?

Yes, mass does impact the speed of an object on a ramp. The heavier the object, the slower it will move down the ramp. This is because of the force of gravity, which is directly proportional to an object's mass.

## 2. How does the angle of the ramp affect the speed of an object?

The angle of the ramp also affects the speed of an object. The steeper the ramp, the faster the object will accelerate down it. This is because the steeper angle increases the force of gravity acting on the object.

## 3. Is the speed of an object on a ramp constant?

No, the speed of an object on a ramp is not constant. As the object moves down the ramp, its speed will change depending on factors such as mass, angle of the ramp, and friction. However, the acceleration of the object remains constant as long as these factors do not change.

## 4. How does friction affect the speed of an object on a ramp?

Friction can significantly impact the speed of an object on a ramp. Friction is the force that opposes motion, and it acts in the opposite direction of the object's movement. The higher the friction, the slower the object will move down the ramp. This is because friction reduces the overall force acting on the object, making it harder to overcome gravity.

## 5. Can an object reach a constant speed on a ramp?

Yes, an object can reach a constant speed on a ramp. This is known as the terminal velocity, which is the maximum speed an object can reach while falling due to the balance between gravity and air resistance. The terminal velocity of an object on a ramp will depend on its mass, angle of the ramp, and friction.

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