Cyclist cycling in a perfect circle - find radius

[Woody11]

I am doing a Biomechanics course and it is just like physics. I don't have a large back ground when it comes to physics. So I need some help. I am having a problem with a question on an assignment. This is the question:

A 78 kilogram cyclist is cycling in a perfect circle, with a velocity of 12m/sec. If The cyclist is leaning at 30 degrees and is in a perfect equilibrum, what is the radius of the circle they are cycling around?

It doesn't seem to be a hard question, but I have been trying to figure this out for about 5 hours now and nothing is hitting me on how to do it. I know it has to deal with centripetal force and I think I should be using the formula F=mv2/r at some point. But I have no idea what the first step is. I hope someone can help me get started, remember I have very little background when it comes to physics it has been a while since I have done it.

Thanks,
Woody

 

[xanthym]

A 78 kilogram cyclist is cycling in a perfect circle, with a velocity of 12m/sec. If The cyclist is leaning at 30 degrees and is in a perfect equilibrum, what is the radius of the circle they are cycling around?

Because rider is in equilibrium at 30 deg to the VERTICAL, the road surface applies Force "F" (shown in drawing below) whose components are sufficient to balance rider's gravitational force (m*g) and provide centripetal force (m*v²/r) required for uniform circular motion. Force "F" components are shown in the drawing. Thus, for equilibrium:
{Centripetal Force} = {"F" Horizontal Component}
::: ⇒ m*v²/r = m*g*tan(30)
::: ⇒ r = v²/{g*tan(30)}
::: ⇒ r = (12 m/sec)²/{(9.81 m/sec²)*tan(30)}
::: ⇒ r = (25.4 meters)

                       ^         ^
                       |        /  
                       |       / [B]F[/B]
                       |  30  /
                       |     /
                   m*g |    / m*g/cos(30)
                       |   /
                       |  /
                       | /
                       |/________>
 
                        m*g*tan(30)               


            Road Surface Force Components On Rider

 

[thepatientmental]

Hello Woody,

First of all, don't worry if you don't have a strong background in physics. Biomechanics and physics go hand in hand, and it's perfectly normal to need some help with understanding concepts and solving problems.

For this question, you are correct in thinking that you will need to use the formula F=mv^2/r. This is known as the centripetal force formula and is used to calculate the force required to keep an object moving in a circular motion.

The first step is to identify the known values in the problem. In this case, we know the mass of the cyclist (m=78kg), the velocity (v=12m/sec), and the angle at which the cyclist is leaning (30 degrees). We also know that the cyclist is in perfect equilibrium, meaning that the forces acting on them are balanced.

Next, we need to draw a free body diagram to visualize the forces acting on the cyclist. In this case, there are two forces acting on the cyclist: the centripetal force (F) and the force of gravity (mg). The force of gravity is acting downwards, while the centripetal force is acting towards the center of the circle.

Now, we can use the formula F=mv^2/r to solve for the radius. Since the cyclist is in equilibrium, the centripetal force must be equal to the force of gravity. So, we can set up the following equation:

F=mg=mv^2/r

We can rearrange this equation to solve for r:

r=mv^2/mg

Plugging in the known values, we get:

r=(78kg)(12m/sec)^2/(78kg)(9.8m/s^2)

Simplifying, we get:

r=14.4m/s^2/9.8m/s^2

r=1.47m

So, the radius of the circle that the cyclist is cycling around is approximately 1.47 meters.

I hope this helps you understand the problem and how to approach it. Remember, it's always helpful to draw diagrams and identify known values before solving a physics problem. Good luck with your assignment!