A small block of mass m = 255 g is released from rest at point along the horizon
ID: 1367553 • Letter: A
Question
A small block of mass m = 255 g is released from rest at point along the horizontal diameter on the inside of a frictionless, hemispherical bowl of radius R = 32.0 cm as shown in the figure below. Calculate the gravitational potential energy of the block-Earth system when the block is at point relative to point . Calculate the kinetic energy of the block at point .Calculate its speed at point .m/s Calculate its kinetic energy when the block is at point . Calculate the potential energy when the block is at point .Explanation / Answer
a) the gravitation potential energy will be mgr ( considering the lowest point with zero potential energy)
so , GPE = 0.225 * 9.8 * 0.32 cm = 0.7056 J
b) kinetic energy at point B = potential energy at highest point A = 0.7056 J
c) now kinetic energy is given by , 0.5 mv2 = 0.7056
=>v2= 6.272
=> v= 2.504 m/s
d) at point C
kinetic enrgy + potential enrgy at C = total potential enrgy at A
=> 0.5* mv2 + m* g* 2/3 * R= 0.7056
=>0.5 * 0.225 *v2 + 0.225 *9.8 * 2/3 *0.32 = 0.7056
=>0.5 * 0.225 *v2= 0.2352
=> v= 1.445 m/s
e) mg * HC = m* g* 2/3 * R = 0.225* 9.8*2/3*0.32 = 0.4704 J