Mechanics quesiton. Skateboarder on ramp.

[milan.007]

Homework Statement

A skateboarder with total mass of 70kg starts from rest at the top of a ramp and accelerates down it. The ramp is 25m long and is at an angle of 20 degrees to the horizontal. The skateboarder has a velocity of 12.2m/s at the bottom of the ramp.


Calculate
i) the average acceleration of the skate boarder on the ramp.
ii) the component of the skateboarders weight that is parallel to the ramp.
iii) the force of riction acting on the skateborader on the ramp.

The skateboarder then maintains a speed of 10.5m/s until he enters a circular ramp of radius 10m.
What is the initail centripetal force on him?
What is his maximum height achieved?

Homework Equations

The Attempt at a Solution

I used v^2 = u^2 + 2as to get the acceleration
I i found his weight 686N and used sin21=686/x, to find the parallel component.
Then for friction i substituted the parelel component from his weight (i think this is wrong).

For the second part, i used F=mv^2/r to find the centripetal force.
Thn i used 1/2mv^2 = mgh to ind the height.

Can someone do it and tell me if i used the correct formulas and please write the answers i want to compare them.

 

[RoyalCat]

You're on the right track, you got the first question right.
a_average = v_f²/2s (Since v_i=0)

I lost you at how you found the parallel component, though, try making a free body diagram of the skateboarder, and breaking mg down into its parallel and orthogonal components, relative to the ramp, using the 20° slope.

For the third question, I would approach with caution. Look at your free body diagram and your answers for questions i and ii.
Hint:

Spoiler

This will come in handy here: ΣF = m*a

As for the second question, could you please define it a bit more clearly? Does the friction continue to act on him? Because if so, then this question requires an integral of the force of friction to solve (If I remember the solution correctly), and I doubt that's what the teacher's aiming for, judging by the other questions.

Assuming there's no friction though, then yes, your solution looks correct. :)

 

[milan.007]

k thanks