A marble is placed at the top of an inverted hemispherical bowl of radius R = 0.30 m. It starts from rest and slides down the bowl without friction. Draw a free body diagram when the marble reaches an angular position θ = 16.6°. From your FBD, sketch the approximate direction of the acceleration.
1.Calculate the radial component of the acceleration (assuming that the radius of the marble is negligible). (Hint: First find the velocity at θ = 16.6°.)
2. What is the tangential component of the acceleration when θ = 16.6°? (Hint: Use Newton's second law.)
3. What is the magnitude of the normal force when the marble loses contact with the bowl?
4. Draw a free body diagram for the angular position where the marble loses contact with the bowl. Draw the direction of the acceleration next to your FBD. What is the angle θ when the marble loses contact with the bowl?
PE = mgh
KE = 1/2mv²
ΔE = ΔKE + ΔPE
F = ma
ac = v²/r
The Attempt at a Solution
1. I found the radial acceleration to be 0.817 m/s² by using ΔE = ΔKE + ΔPE and found v final. I then used ac = v²/r
2. Tangential acceleration is 2.80 m/s² which I found by using ƩFx= Nx -> ma = mgsin(16.6)
3. Normal force is 0
4. I am not sure how to find this value. I tired to find the velocity when the marble loses contact and sub that into ΔE = ΔKE + ΔPE to find the final height but I wasn't sure how to find the velocity or if this is even the correct method.