A group of students perform the same \"Conservation of Mechanical Energy\" exper

ID: 1443296 • Letter: A

Question

A group of students perform the same "Conservation of Mechanical Energy" experiment that you performed in lab by allowing a solid sphere and then a solid cylinder to roll down the ramp. The solid sphere was released from a height of 14.3 cm. From what height hcylinder should the solid cylinder be released so that it has the same speed as the solid sphere when it reaches the bottom of the ramp?
A group of students perform the same "Conservation of Mechanical Energy" experiment that you performed in lab by allowing a solid sphere and then a solid cylinder to roll down the ramp. The solid sphere was released from a height of 14.3 cm. From what height hcylinder should the solid cylinder be released so that it has the same speed as the solid sphere when it reaches the bottom of the ramp?
A group of students perform the same "Conservation of Mechanical Energy" experiment that you performed in lab by allowing a solid sphere and then a solid cylinder to roll down the ramp. The solid sphere was released from a height of 14.3 cm. From what height hcylinder should the solid cylinder be released so that it has the same speed as the solid sphere when it reaches the bottom of the ramp?
A group of students perform the same "Conservation of Mechanical Energy" experiment that you performed in lab by allowing a solid sphere and then a solid cylinder to roll down the ramp. The solid sphere was released from a height of 14.3 cm. From what height hcylinder should the solid cylinder be released so that it has the same speed as the solid sphere when it reaches the bottom of the ramp?

Explanation / Answer

Using energy conservation

I for solid sphere = (2/5)mr^2

I for cylinder = (1/2)mr^2

For the sphere
mgH = 0.5mv^2 + 0.5*Iw^2
2mgH = mv^2 + (2/5)*mv^2 ( since v = wr)
cancel m
(10/7)*gH = v^2
Same procedure for cylinder
For the cylinder
mgh = 0.5*mv^2 + 0.5*Iw^2
2mgh = mv^2 + 0.5*mv^2
(4/3)*gh = v^2
If each velocity is the same then
(4/3)gh = (10/7)gH
h = (30/28) H = 30*0.143/28 = 15.32 cm

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A group of students perform the same \"Conservation of Mechanical Energy\" exper

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