Use the figure to the right for the next problem. A flexible rope of mass m and length L = L 1 + L 2 , hangs over a frictionless peg, as shown in the figure
-What is the speed of the rope when it just slides off the peg?

Question

Quizplus · Accepted Answer

The rope will slide off the peg when the tension in the rope at the peg becomes zero. We can use the principle of conservation of energy to find the velocity of the rope at this point. The potential energy of the rope at the initial position is given by:
U = mgh = mg(L/2)

As the rope slides off the peg, the potential energy of the rope gets converted into kinetic energy. At the point when the tension in the rope at the peg becomes zero, all the potential energy has been converted into kinetic energy, so we have:
U = K
mg(L/2) = (1/2)mv^2

Solving for v, we get:
v = sqrt[(2gL)/2] = sqrt(gL)

Substituting the given values, we get:
v = sqrt[(10 m/s^2)(5 m)] = sqrt(50) m/s = 7.07 m/s

The closest answer choice is B: 11eaa331_f519_e022_9fad_43383d826c39_TB6079_11.

Use the Figure to the Right for the Next Problem