The graph above represents the potential energy U as a funct

The graph above represents the potential energy U as a function of position r for particle is released from rest at position r_0, what will its speed be at position 3r_0? a. squareroot 8U_0/m b. squareroot 2U+0/m c. squareroot 2U_0/m d. squareroot 6U_0/m

Solution

at r = r0 :

PE = 3U0

KE = 0

at r = 3r0 :

PE = 2U0

KE = m v^2 /2

Applying energy conservation,

3U0 + 0 = 2U0 + m v^2 /2

m v^2 /2 = U0

v = sqrt[ 2 U0 / m ]

Ans(c)