Mechanics problem - Tricycle?

Question

http://s76.photobucket.com/albums/j29/E_man777/?action=view¤t=tricycle_l.jpg

On the tricycle above, the pedals are locked to the wheel.
What happens when the Force pulls in the picture above and why?

- I think that the wheel will spin the other way, making the tricycle drive backwards. Is this correct?

Thank you for the help

Answer 1

You are incorrect. Though it may seem counterintuitive, the tricycle STARTS to move forward, WHETHER there is friction or NOT!

The full analysis with the rest of the tricycle considered is a bit messy, so let's consider just a bare wheel with fixed attached cranks. (I think you'll agree that that still contains the same apparently counterintuitive or paradoxical elements.) I'll also consider only the initial effects. Consider the two extreme cases.

a). No friction. Clearly, without friction, the force F will simply start to accelerate the whole wheel forward, with no wheel rotation.

b). Sufficient friction at the wheel's point of contact with the road to prevent sliding.

Let the wheel's radius be ' a,' and the forward facing, horizontal force F be applied at a crank length of r from its axle. If the wheel's mass is ' m,' the wheel will have some moment of inertia M.I. of kma^2 around the axle, and therefore an M.I. of (k + 1) ma^2 about the road's point of contact (by the parallel-axis theorem).

Then taking moments about the point of contact, there's only a moment F (a - r) tending to make it roll FORWARD.
Let x be a coordinate in the forward direction, and θ an angle of rotation that will increases as x increases in that same direction. Since a d^2 θ / dt^2 = d^2 x /dt^2, one will get

(k + 1) m a^2 d^2 θ / dt^2 = (k + 1) m a d^2 x /dt^2 = F (a - r).

Because a > r, θ and x both start to increase.

[Note the clear implication: if r > a, that is if the crank could be extended so as to have F pulling BELOW the ground level, then the wheel/tricycle would INDEED go BACKWARDS! In fact, since posting this answer, I have come across a web site showing the cases r <, =, and > a. See ### in "source" below.]

Notice that the point of attachment of the force F ALSO MOVES FORWARD. How so?: Because as the wheel's centre moves forward a small distance a Δθ, the point of attachment rotates in the "negative x direction" relative to the centre, through a distance r Δθ. So the net distance the point of attachment moves forward is

(a - r) Δθ,

again a positive amount, a fraction (a - r)/a of the distance Δx that the centre of the wheel moves forward. That means, quite sensibly, that as (a part of) the force F is accelerating the wheel forward, it is doing POSITIVE work, that is: moving the point of application forward, as indeed it must!

Notice again that only a part or FRACTION of F is actually accelerating the whole wheel forward. How so? Because there is a BACKWARDS frictional force G at the point of contact. By choosing to take moments about that point of contact, I was able to eliminate G from the above considerations. However, if one now switches attention to the linear, forward acceleration, or alternatively considers moments about the CENTRE of the wheel, one can determine how big G is. The reduction in F depends upon both (a - r) and upon k, but I think you'll find that you can formally work out the same, self-consistent value of G by either of the two approaches suggested.

Admittedly I simplified the analysis by only treating a bare wheel plus fixed attached cranks. However, it has the same seemingly paradoxical elements in it.

Live long and prosper.

Answer 2

Dr Spock is right. the error is thinking of the wheel hub as stationary. rather as the force pulls on the trike, it can go forward. the path that the pedal takes is shaped kind of like the scalloped top of a fence, a series of bumps. so the force will make the pedal move forward, but the bottom the wheel will stay still on the ground, so the center hub of the wheel will move forward faster than the pedal does. hopefully that can be imagined....

Answer 3

yes it will just rotate backward which produces friction to the ground but the trike is stationary until the pedal reach the horizontal position and the force applied if stronger will just drag the trike forward with stationary front wheel that only produces friction to the ground and the rear wheels rotating forward

Answer 4

contact with  http://www.3wheelermotorcycle.com/