Question

As shown in the figure below, a small item is released from rest at point A along the horizontal diameter on the inside of a frictionless, hemispherical bowl. The item has a mass m = 155 g and the bowl has a radius R 33.0 cm. 2R/3 (a) Calculate the gravitational potential energy of the item-Earth system (in J) when the item is at point A relative to point B. J (b) Calculate the kinetic energy of the item (in J) at point B. (c) Calculate its speed (in m/s) at point B. m/s (d) Calculate its kinetic energy (in J) when the item is at point C TH (e) Calculate the potential energy (in )) when the item is at point C tpla hile re Need Help? Read It irt a Tel e s

Answer 1

a)

Gravitational Potential energy at point A

PE_A=mgR =0.155*9.81*0.33 = 0.50178 J

b)

Kinetic energy at point B is

KE_B=0.50178 J

c)

(1/2)mV_B²=0.50178

V_B=sqrt[2*0.50178/0.155]=2.5445 m/s

d)

Kinetic energy at point C

KE_C=mgR-mg(2R/3) =0.155*9.81*(0.33-(2/3)*0.33)

KE_C=0.16726 J

E)

Potential energy at point C

PE_C=mg(2R/3)=0.155*9.81*(2*0.33/3)=0.33452 J