Ball of mass rolling down an incline

AI Thread Summary
A ball of mass 2.80 kg and radius 0.148 m is released on a 38.0° incline, and the goal is to determine its speed after rolling 1.55 m. The discussion revolves around the application of energy conservation principles, specifically the relationship between potential energy and kinetic energy. The initial potential energy is calculated using the height derived from the incline, while the final energy includes both translational and rotational kinetic energy. The participant expresses uncertainty about their calculations, particularly regarding the potential energy adjustments. Overall, the conversation emphasizes the correct application of energy equations to solve the problem accurately.
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Homework Statement


A ball of mass 2.80 kg and radius 0.148 m is released from rest on a plane inclined at an angle θ = 38.0° with respect to the horizontal. How fast is the ball moving (in m/s) after it has rolled a distance d=1.55 m? Assume that the ball rolls without slipping, and that its moment of inertia about its center of mass is 1.50E-2 kg·m2.
prob30_BallIncl.gif



Homework Equations



KE - kinetic energy
KEr - rotational kinetic energy
PE - potential kinetic energy

KE0 + KEr0 + PE0 = KEf + KErf + PEf

The Attempt at a Solution



I thought I had it right but it seems I went wrong somewhere and I'm assuming that it's probably where the potential energy is concerned. Since, the entire hypotenuse isn't given and all that is given is the distance d, I readjusted the axis for potential energy and made the point where the ball goes down to in the picture the ground level so that PE at that point equals 0. The initial KE is 0 as well as the initial rotational KE, and since I made the final PE equal 0 I got an equation PE0 = KEf + KErf. To find the height for the initial PE I did sin(theta) times the d. I guessing that that's the wrong thing to do. Anyone know the right way to go about it?
 
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help?
 
You have done everything correctly. Repeat the calculations to see if you've made any arithmetical mistake.
 
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