Potential Energy & Conservative Forces #18

[UCrazyBeautifulU]

A skateboard track has the form of a circular arc with a 4.00 m radius, extending to an angle of 90.0° relative to the vertical on either side of the lowest point, as shown in the figure below.


A 55.9 kg skateboarder starts from rest at the top of the circular arc. What is the normal force exerted on the skateboarder at the bottom of the circular arc?

3287 N was not the correct answer.

can anyone give me some pointers on this problem? Sorry I can't post the picture for some reason.

I was figuring it out this way, but it isn't right:
the normal force exerted on the skateboarder at the bottom of the circular arc = 6mg
= 55.9 x 6 x 9.8 N

 

[Doc Al]

Use Newton's 2nd law (as well as conservation of energy). What forces act on the skateboarder at the point in question? Hint: The acceleration is centripetal.

 

[radou]

Where did you get 6mg from? First, use the fact that the work done by gravity from the top to the bottom equals the change of kinetic energy to obtain the speed at the bottom of the arc. Knowing the speed, you can calculate the centripetal force. You know the weight, so it shouldn't be difficult to calculate the normal force.

 

[UCrazyBeautifulU]

how do i figure out the velocity and the acceleration?

I need the velocity for the centripetal force equation & I need the acceleration for the f=ma equation.

thanks so much.

 

[Doc Al]

how do i figure out the velocity

Conservation of energy, as radou described.

and the acceleration?

What's the formula for centripetal acceleration?

Hint: Solve the problem algebraically (using symbols) until the last step.

 

[UCrazyBeautifulU]

f_cp = ma_cp = mv^2 / r

okay, I still have the velocity missing in this equation, so what do I do?

 

[Doc Al]

Use conservation of energy! How far does the skater fall? What's his decrease in gravitational PE? His increase in KE?

 

[UCrazyBeautifulU]

what's the equation i should use?

 

[UCrazyBeautifulU]

what's the conservation of energy equation i should use? thanks.

 

[Doc Al]

$$\Delta {PE} + \Delta {KE} = 0$$