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A small block of mass m = 270 g is released from rest at point (A) along the hor

ID: 1903458 • Letter: A

Question

A small block of mass m = 270 g is released from rest at point (A) along the horizontal diameter on the inside of a frictionless, hemispherical bowl of radius R = 31.5 cm as shown in the figure below.


(a) Calculate the gravitational potential energy of the block-Earth system when the block is at point (A) relative to point (B). _______________J ???

(b) Calculate the kinetic energy of the block at point (B) ________________J ???

(c) Calculate its speed at point (B) ______________m/s ???

(d) Calculate its kinetic energy when the block is at point (C) ___________J ???

(e) Calculate the potential energy when the block is at point (C) ___________J ???

Explanation / Answer

a.)

at point B, assuming potential energy is zero.

so gravitation potential energy at point a relative to point b is mgR.

= 0.27*9.8*0.315

=0.833 J

c.)

0+mgR = 1/2 mvb^2 + 0

vb = sqrt(2gR)

vb = 2.48 m/s

b.)

1/2 mvb^2

=0.5*0.27*2.48^2

=0.83J

e.)

potential enery = mg(2R/3)

= 0.27*9.8*0.67*0.315

=0.56 J

d.)

Ke = 0.5(0.27*2.48^2) - 0.56 = 0.27J