Loop-the-Loop: Net Force on a Ball Moving on a Vertical Loop

[KCEWMG]

Homework Statement

A small ball of mass m = 0.150 kg is sliding along a frictionless loop-the-loop. The loop-the-loop is standing on a table such that the plane of the loop is vertical. The loop has a radius of r = 0.200 m. What is the magnitude of the net force acting on the ball when it is on the right side and half-way up the loop, and moving upward with a speed of 2.00 m/s?

Homework Equations

F=ma
Centripetal Acceleration= v^2 / r

The Attempt at a Solution

Alright, here's what I've tried:
I drew a free body diagram. Facing down, I put 9.8*.150=1.47 thinking about the gravitational force. I then used the Centripetal Acceleration equation,t (2.00^2)/.2, which resulted in 20. I then multiplied this by the mass and got 3. 3-1.47 is equal to 1.53 N, which is not the correct answer. The correct answer is 3.34 N.
Where am I going wrong?

 

[TaxOnFear]

Hey KCEWMG.
I think I have the solution. You're trying to add/subtract the forces acting on the ball to get the overall/resulting force acting on it, however the forces aren't collinear, therefore you can't do that. Draw you're free body diagram, with mg in the negative y direction, and the force due to the centripetal acceleration in another direction (think about it, it's always accelerating towards the centre of the of the loop-to-loop).

Hope this helps.

 

[KCEWMG]

Ahh, gotcha.
CENTRIPETAL Acceleration. Thanks!