Question

ROPE (initially vertical) vA flexible, uniform rope of mass m and length L is initially held motionless over frictionless ice, with one end just touching the ice. At the bottom of the rope is a very small, frictionless ramp that causes the rope to end up sliding horizontally on the ice with velocity v. What is the magnitude of v?

Answer 1

Answer:

$V=\sqrt {Lg}\ m/s$

Explanation:

Given that

Mass = m

Length =L

When rope is vertical then potential energy

u₁ = m g h            

h = L/2    Center of mass of rope is at L/2 distance from ground.          

u₁ = m g L/2            

The final potential energy

u₂=0  (because h will become zero)

Lets the speed speed become V

From energy conservation

$mg\dfrac{L}{2}=\dfrac{1}{2}mV^2$

$V=\sqrt {Lg}\ m/s$