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A small block of mass m = 200 g is released from rest at point Ⓐalong the horizontal diameter on the inside of a frictionless, hemispherical bowl of radius R = 30.0 cm (Fig. P8.41). Calculate (a) the gravitational potential energy of the block-Earth system when the block is at point Ⓐ relative to point Ⓑ, (b) the kinetic energy of the block at point Ⓑ, (c) its speed at point Ⓑ, and (d) its kinetic energy and the potential energy when the block is at point Ⓒ.

Verified Answer :

MissPhiladelphia
AThe potential energy at point A is
PE = mgh = 0.2 (9.81) (0.3)
PE = 0.59 J

b. At the bottom, since the surface is frictionless, the potential energy is completely converted to the kinetic energy, thus,
KE = 0.59 J

c. The speed of the object can be calculated using:
KE = (1/2)mv^2
0.59 = (1/2)(0.2)(v)^2
v = 2.43 m/s

d. The location of point c is unknown but it can be derived using the formula:
mg(R-h) = KE
where R is the radius and h is the vertical distance of the object from the bottom.