Fundamentals of Physics 10e , Halliday. End of Chapter Question 11. A cannonball
ID: 1537130 • Letter: F
Question
Fundamentals of Physics 10e , Halliday. End of Chapter Question 11. A cannonball and a marble roll smoothly from rest down an incline. a) Is the cannonball's time to the bottom more than, less than, or the same as the marble's, and b) Is the cannonball's translational kinetic energy at the bottom more than, less than, or the same as the marble's? The answers provided by the text for both the a) and b) are the "same".
a) I think I understand why the answer is the same. Since acomx= (g Sin x)/(1+ Icom/MR2) and Icom = 2/5 MR2 then acomx is the same for both the cannonball and the marble and therefore they reach bottom at the same time.. Is this the correct way to prove they reach the bottom at the same time?
b) I don't understand how the cannonball and the marble can have the same translational KE when translational KE = 1/2MV2. Please explain how the cannonball and the marble can have the same translational KE,.
Explanation / Answer
b) as both have same acceleration and reach at the bottom at the same time, so both must have the same velocity also. so for having same translational KE the only thing required is that both should have the same mass. If the masses are same, translational KE will be same.
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