In this lab, we seek to prove that angular and linear momentum are conserved in a system.
The system in question is a ball which rolls without slipping down a ramp and collides inelastically with a disk that spins horizontally with no friction. The motion of this system is in 2 parts
First, the ball rolls down the ramp, and in doing so its GPE is converted to rotational and translational KE
Mgh=1/2mv^2+1/2I(omega)^2
Second, the ball collides with the spinning disk, linear momentum of the ball is converted to rotational momentum of the disk and ball.
m(v/r)=I(disk+ball)(omega)
In order to find the actual initial velocity of the ball once it exits the ramp, we let the ball go down the ramp and land on the floor. We measure the distance from the edge of the ramp (superimposed on the floor) that the ball travels before hitting, and the height of the edge of the ramp. We then use kinematics equations to determine the exit velocity.
In order to find inertia of the disk we use a hanging mass attached to it in the same way that we did in earlier experements with this aparatus. We then measure angular acceleration and use T=I(alpha) equation to find I.
Our calculations are below
As we can see, there is a large discrepancy between the theoretical initial exit velocity of the ball and the actual velocity. This indicates that the ball does not roll without slipping. Our theoretical value for omega final is 2/43 rad/s
We then run the experement and measure angular velcocity, which turns our to be 1.87 rad/s.
The large difference between our actual and expected values for omega are probably due to the issue of the ramp not allowing the ball to roll without slipping.
The system in question is a ball which rolls without slipping down a ramp and collides inelastically with a disk that spins horizontally with no friction. The motion of this system is in 2 parts
First, the ball rolls down the ramp, and in doing so its GPE is converted to rotational and translational KE
Mgh=1/2mv^2+1/2I(omega)^2
Second, the ball collides with the spinning disk, linear momentum of the ball is converted to rotational momentum of the disk and ball.
m(v/r)=I(disk+ball)(omega)
In order to find the actual initial velocity of the ball once it exits the ramp, we let the ball go down the ramp and land on the floor. We measure the distance from the edge of the ramp (superimposed on the floor) that the ball travels before hitting, and the height of the edge of the ramp. We then use kinematics equations to determine the exit velocity.
In order to find inertia of the disk we use a hanging mass attached to it in the same way that we did in earlier experements with this aparatus. We then measure angular acceleration and use T=I(alpha) equation to find I.
Our calculations are below
As we can see, there is a large discrepancy between the theoretical initial exit velocity of the ball and the actual velocity. This indicates that the ball does not roll without slipping. Our theoretical value for omega final is 2/43 rad/s
We then run the experement and measure angular velcocity, which turns our to be 1.87 rad/s.
The large difference between our actual and expected values for omega are probably due to the issue of the ramp not allowing the ball to roll without slipping.
It would be good to see the final graph to tell what omega final actually was, to compare with the 1.87 you predicted.
ReplyDeleteThe R for the ball was not 0.07 cm--that would have ben a ball 5' in diameter. The "R" was where the ball landed relative to the axis of rotation of the disk.