Newton's Laws of motion -- Bicyclist pedaling up a slope

[PeroK]

The question asks for the net force from the bike on the biker (in the travel direction).

No it doesn't. That's not what the question asks at all.

That's the question that would yield the given answer.

 

[Orodruin]

No it doesn't. That's not what the question asks at all.

That's the question that would yield the given answer.

Well, as I pointed out in the beginning, the actual question quoted is badly worded and nonsense. If you are going to debate a nonsense question you will end up with nonsense and differing interpretation. I see no point in preferentially interpret ”providing force” as ”force used to propel the bike”. With that in mind, we have to attempt to interpret the question in the light of what the person posing the question wanted for an answer.

 

[bob012345]

Well, as I pointed out in the beginning, the actual question quoted is badly worded and nonsense. If you are going to debate a nonsense question you will end up with nonsense and differing interpretation. I see no point in preferentially interpret ”providing force” as ”force used to propel the bike”. With that in mind, we have to attempt to interpret the question in the light of what the person posing the question wanted for an answer.

The actual question made perfect sense to me. Just how would you have worded it to the student?

 

[Orodruin]

The actual question made perfect sense to me. Just how would you have worded it to the student?

”What is the component of the net force with which the biker acts on the bike in the direction of travel?”

As we have witnessed in this thread, the word ”provides” is not standard nomenclature and has caused a wide range of opiniated interpretations.

 

[jbriggs444]

The actual question made perfect sense to me. Just how would you have worded it to the student?

The question seemed badly strained to me.

As asked: "How much force does he provide"

As a native English speaker, the implication of "provide" is something the rider does beyond just sitting on the seat. As a reader, the obvious interpretation would then be that the rider "provides" motive power. He pedals. However that was not the writer's intent. [The astute reader realizes that the problem does not specify a gear ratio, and assumes that the writer intended the problem to be solvable. So the natural reading cannot be the intended one]

I would ask "What is the net force of rider on cycle in the direction of the upward slope?"

Or I might be trickier. Just "What is the net force of rider on cycle" and expect the correct answer to be in the form of a vector that might be expressed in a number of possible formats.

 

[Orodruin]

The answer is the same. But saying that the driver provides the force in this case is, I would say, simply wrong.

Disagree. Your beef is with the word ”provide” which does not have a standard meaning and even if you do interpret it as the force putting energy into the system it still makes the question unanswerable without further specification of gears etc. Making it pretty clear that this is not the intended interpretation.

 

[erobz]

[The astute reader realizes that the problem does not specify a gear ratio, and assumes that the writer intended the problem to be solvable. So the natural reading cannot be the intended one]

I'm having trouble seeing how the gear ratio comes into play. The force accelerating the rider at $-0.3 \rm{\frac{m}{s^2}}$ doesn't care what gear the bike is in. What force acting on the bike does?

 

[PeroK]

I'm having trouble seeing how the gear ratio comes into play. The force accelerating the rider at $-0.3 \rm{\frac{m}{s^2}}$ doesn't care what gear the bike is in. What force acting on the bike does?

The force applied to the pedals. Which is, of course, a critical factor for the cyclist.

 

[Orodruin]

I think we should also not rule out the possibility that the original problem was not posed in English and that ”provide” is simply a matter of a faulty translation and that the translation for the correct interpretation would be ”exert”.

(”Provide” could very well be the literal translation of the original word without being correct in the current technical setting)

 

[erobz]

The force applied to the pedals. Which is, of course, a critical factor for the cyclist.

Ok, I think I'm seeing it. That force applied to the pedals can grow in the direction normal to the slope due to the gear ratio.

 

[PeroK]

Ok, I think I'm seeing it. That force applied to the pedals can grow in the direction normal to the slope due to the gear ratio.

Or reduce. That's the purpose of low gears.

 

[Orodruin]

Or reduce. That's the purpose of low gears.

Give me a fulcrum and a lever and I shall move the Earth.

 

[erobz]

Or reduce. That's the purpose of low gears.

What gears do wasn't my issue of contention. It was the interplay between the various forces that is the subtle bit to me.

If this is a person cycling on horizontal ground (while sitting) with acceleration $a$ and $F_p$ changes from a change in gears, the only other force that can change is $N$ in this model. This is what I was not initially picking up...not "what gears do".

 

[Orodruin]

What gears do wasn't my issue of contention. It was the interplay between the various forces that is the subtle bit to me.

View attachment 317055

If this is a person cycling on horizontal ground (while sitting) with acceleration $a$ and $F_p$ changes from a change in gears, the only other force that can change is $N$ in this model. This is what I was not initially picking up...not "what gears do".

That’s not a very accurate model to be honest. All of those forces except weight will generally be in other directions. Weight will generally not be concentrated right above the saddle. The typical connection at the steering rod is leaning on it, making the force from the rod be up and backwards.

 

[PeroK]

What gears do wasn't my issue of contention. It was the interplay between the various forces that is the subtle bit to me.

View attachment 317055

If this is a person cycling on horizontal ground (while sitting) with acceleration $a$ and $F_p$ changes from a change in gears, the only other force that can change is $N$ in this model. This is what I was not initially picking up...not "what gears do".

If you imagine a bike suspended above the ground, then there would be no linear motion, but the force on the pedals would drive a rotation of the back wheel. The ratio of rotation of the pedals to rotation of the back wheel is critical. Unless the back wheel slips then this determines the speed of the bicycle when accelerating or going uphill. That determines the force required to move the pedals, notably when starting from rest.

 

[erobz]

That’s not a very accurate model to be honest.

I still think it captures the basic idea. You can ride a bike like that. Sit on the seat, arms in tension as a two force member (fixed by rider + bike geometry), pedals pivot and the applied force stays pretty vertical on them. The part with the weight being not directly above the saddle...I'm not analyzing torques? There are some friction forces missing at the saddle and the pedal, but they would be fixed by the acceleration. If you rapidly change to a high gear and try to maintain acceleration you can start to come off the seat. I never said it was accurately capturing all ways of riding a bike...it's a crude model, first round draft to get some insight (probably my only one though).

If you feel it does serious injustice and want to show how the full analysis differs, I'm all ears.

 

[bob012345]

Give me a fulcrum and a lever and I shall move the Earth.

All I have to do to move the Earth is to stand up.

 

[jbriggs444]

I still think it captures the basic idea. You can ride a bike like that. Sit on the seat, arms in tension [...]

In my experience, the arms are normally in compression and provide some of the support for the upper body. If one "stands up" on the pedals then the seat ceases to be a factor and the arms go into tension, alternating right and left in synch with the cadence.

 

[erobz]

In my experience, the arms are normally in compression and provide some of the support for the upper body. If one "stands up" on the pedals then the seat ceases to be a factor and the arms go into tension, alternating right and left in synch with the cadence.

Fine, lets ride without hands then. We can even lean forward a bit to balance the torques.

 

[erobz]

In my experience, the arms are normally in compression and provide some of the support for the upper body. If one "stands up" on the pedals then the seat ceases to be a factor and the arms go into tension, alternating right and left in synch with the cadence.

I just went and checked. I definitely feel tension (not compression) in my arms while seated and accelerating on my Mt. bike. I think the position you are describing is what riding at constant velocity feels like.

 

[jbriggs444]

I just went and checked. I definitely feel tension (not compression) in my arms while seated and accelerating on my Mt. bike. I think the position you are describing is what riding at constant velocity feels like.

On average, you are at constant velocity.

 

[erobz]

On average, you are at constant velocity.

Ok, but I'm not on average at constant velocity while I'm accelerating. You are saying most of the time while riding "normally" you are at constant velocity. I say that depends on the riding you are doing. For instance, I ride downhill mountain biking ( like Red Bull Rampage ). Most of the time on a bike in that type of riding is spent accelerating. Obviously in that type of riding it's a mix of tension and compression depending on whether or not I'm descending or jumping.

 

[haruspex]

Ok, but I'm not on average at constant velocity while I'm accelerating. You are saying most of the time while riding "normally" you are at constant velocity. I say that depends on the riding you are doing. For instance, I ride downhill mountain biking ( like Red Bull Rampage ). Most of the time on a bike in that type of riding is spent accelerating. Obviously in that type of riding it's a mix of tension and compression depending on whether or not I'm descending or jumping.

we seem to be getting further and further from the original question. How about a separate thread?

 

[erobz]

we seem to be getting further and further from the original question. How about a separate thread?

No need for that, I’ll let it be.