Activity: Rolling Energy Conservation Grade (0-6) Petunia the Spherical Pig NAME

Question

Activity: Rolling Energy Conservation Grade (0-6) Petunia the Spherical Pig NAME (print) Petunia the spherical pig starts from rest and rolls without slipping down path (e) to the bottom of a hill. She is a solid sphere with a radius of R and a mass of M and sits on a hillside with a height of h. a) What is her initial total mechanical energy E? b) Write an expression for her total kinetic energy at the bottom (translational plus rotational). Simplify your expression until it is in terms of M, R, and vy only. c) Use your answers above to write the energy conservation equation and solve it for v d) Now plug in numbers: R- 0.25 m and h -2 m and get a number for v e) For which path will her speed at the bottom be the greatest? (Hinit: how does your formula from part (c) depend on the path?) a) path (a) b) path (b) c) path (c)d) all the same e)can't tell

Explanation / Answer

a)

initial mechanical energy = initial Potential energy + initial kinetic energy

since she is at rest initially , hence initial kinetic energy = 0 J

initial mechanical energy = initial Potential energy = Mgh

Ei = Mgh

b)

moment of inertia of soild sphere = I = (0.4) MR2

kinetic energy at the bottom = rotational kinetic energy + translational KE

KEf = (0.5) I wf2 + (0.5) m vf2

KEf = (0.5) (0.4)(MR2) (vf/R)2 + (0.5) M vf2

KEf = (0.2) (Mvf2 ) + (0.5) M vf2

KEf = (0.7) M vf2

c)

using conservation of energy

Total energy at Top = total energy at bottom

Ei = KEf

Mgh = (0.7) M vf2

vf = sqrt((10/7) gh)

vf = sqrt((3.74) gh)

d)

vf = sqrt((3.74) gh)

h = 2 m

vf = sqrt((3.74) gh) = sqrt((3.74) (9.8 x 2)) = 8.6 m/s

e)

the formula is independent of the path , hence speed at the bottom will be same for all the path

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