Ball of mass rolling down an incline

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SUMMARY

A ball with a mass of 2.80 kg and a radius of 0.148 m rolls down an incline at an angle of 38.0°, covering a distance of 1.55 m. The problem involves calculating the final speed of the ball using the conservation of energy principle, where the initial potential energy is converted into translational and rotational kinetic energy. The moment of inertia of the ball is given as 1.50E-2 kg·m². The correct approach involves determining the height of the incline using the sine function and ensuring all energy forms are accounted for in the calculations.

PREREQUISITES
  • Understanding of conservation of energy principles
  • Familiarity with rotational dynamics and moment of inertia
  • Knowledge of trigonometric functions, specifically sine
  • Basic algebra for solving equations
NEXT STEPS
  • Review the conservation of mechanical energy in rolling motion
  • Study the calculation of potential energy using trigonometric functions
  • Learn about the relationship between translational and rotational kinetic energy
  • Explore examples of similar problems involving rolling objects on inclines
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Students studying physics, particularly those focusing on mechanics and energy conservation, as well as educators looking for examples of rolling motion problems.

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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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