Calculating Marble Speed Using Conservation of Energy

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Conservation of Energy-- HELP!

I missed my Physics class where they discussed conservation of energy so I am making al ot of mistakes on my homework. If you could help with the following problem, I would appreciate it.

A marble is rolling down a rollercoaster track. Attached to the track is a CPO timing device that calculates the number of seconds the marble takes to roll through the lightgate. At a given position D on the rollercoaster track, the Potential Energy of the marble is 120 Joules. (I believe that a previous question gave a total energy of 160 Joules for position D). If the radius of the marble is 0.506 cm and the mass of the marble is 0.56 grams, how long does the marble take to pass through the lightgate (seconds).

I initially converted the radius in centimeters into meters and multiplied it by two to get the diameter. I then converted the mass in grams to kilograms and tried to solve for the speed assuming the Kinetic Energy of the marble was 40 Joules (Total Energy - Potential Energy = Kinetic Energy). I used the KE= 1/2 mv^2 formula to solve for v and divided it by the diameter because the marble only moves in increments of its diameter through the lightgate. This supplied me with an unrealistic and WRONG answer for the number of seconds. Is there a better way to do this? Once again, I missed the class and haven't had time to talk to my teacher about it, so PLEASE HELP!

 

[vaishakh]

What is lightgate?

 

[nrqed]

I missed my Physics class where they discussed conservation of energy so I am making al ot of mistakes on my homework. If you could help with the following problem, I would appreciate it.

A marble is rolling down a rollercoaster track. Attached to the track is a CPO timing device that calculates the number of seconds the marble takes to roll through the lightgate. At a given position D on the rollercoaster track, the Potential Energy of the marble is 120 Joules. (I believe that a previous question gave a total energy of 160 Joules for position D). If the radius of the marble is 0.506 cm and the mass of the marble is 0.56 grams, how long does the marble take to pass through the lightgate (seconds).

I initially converted the radius in centimeters into meters and multiplied it by two to get the diameter. I then converted the mass in grams to kilograms and tried to solve for the speed assuming the Kinetic Energy of the marble was 40 Joules (Total Energy - Potential Energy = Kinetic Energy). I used the KE= 1/2 mv^2 formula to solve for v and divided it by the diameter because the marble only moves in increments of its diameter through the lightgate.

I have no idea what you meant by this last statement!

This supplied me with an unrealistic and WRONG answer for the number of seconds. Is there a better way to do this? Once again, I missed the class and haven't had time to talk to my teacher about it, so PLEASE HELP!

It looks as if you have covered energy of rotational motion. Then for the kinetic energy, use $${1 \over 2} m v^2 + {1 \over 2} I \omega^2$$. You can look up the moment of inertia for a sphere. And you should have seen how to relate $$\omega$$ to the speed and the radius of the sphere.

Pat

 

[oooo]

No we haven't done anything with rotational kinetic energy yet. The lightgate is just part of the timer in which the marble rolls through it and it calculates the time that the marble took between entering and exiting the lightgate. The distance it travels in the lightgate is the same as its diameter.

 

[nrqed]

No we haven't done anything with rotational kinetic energy yet. The lightgate is just part of the timer in which the marble rolls through it and it calculates the time that the marble took between entering and exiting the lightgate. The distance it travels in the lightgate is the same as its diameter.

Oh! I see.

Now I understand better. Then what you did seems right.
Of course, you must divide the *diameter* BY the *speed* to get the time (you wrote the inverse!)

Pat

 

[oooo]

Thanks for your help!