- #1
Sonorus
- 2
- 0
A small, solid, uniform ball is to be shot up from point P so it rolls smoothly along a horizontal path, up along a ramp, and onto a plateau. Then it leaves the plateau horizontally to land on a game board, at a horizontal distance (d=6cm) from the right edge of the plateau. The vertical height from P to the top of the plateau is 5 cm, and the game board is s 1.6 cm down from the top of the plateau. A MS paint diagram can be found here: http://imgur.com/rCCPq
Find the speed at witch the ball will be shot at P so it lands 6cm from the plateau.
Relevant equations:
Kinetic energy=.5(Inertia of center of mass)(angular velocity)^2+.5(mass)(velocity)^2
w=angular velocity
I=Inertia of center of mass
So, I've got the basic idea of the problem. I've found the required velocity as the ball leaves the plateau to land in the right spot with projectile motion. Now I'm supposed to use conservation of energy to find the initial velocity.
I don't know exactly how to proceed. The ball starts rotating immediately, so I'd have to include rotational kinetic energy in both in the energy at P, and at the top of the plateau, correct?
So does this look correct? I'm also not sure how to find the inertia used in these equations, so I'd appreciate help with that.
Energy@P= .5(mv^2) +.5(I)(w^2) (only kinetic energy)
Energy@plateu = .5(mv^2)+.5(I)(w^2)+mgy (kinetic energy +potential)
Find the speed at witch the ball will be shot at P so it lands 6cm from the plateau.
Relevant equations:
Kinetic energy=.5(Inertia of center of mass)(angular velocity)^2+.5(mass)(velocity)^2
w=angular velocity
I=Inertia of center of mass
So, I've got the basic idea of the problem. I've found the required velocity as the ball leaves the plateau to land in the right spot with projectile motion. Now I'm supposed to use conservation of energy to find the initial velocity.
I don't know exactly how to proceed. The ball starts rotating immediately, so I'd have to include rotational kinetic energy in both in the energy at P, and at the top of the plateau, correct?
So does this look correct? I'm also not sure how to find the inertia used in these equations, so I'd appreciate help with that.
Energy@P= .5(mv^2) +.5(I)(w^2) (only kinetic energy)
Energy@plateu = .5(mv^2)+.5(I)(w^2)+mgy (kinetic energy +potential)