Question

Shown below is a box of mass m1 that sits on a frictionless incline at an angle above the horizontal θ=30°. This box is connected by a relatively massless string, over a frictionless pulley, and finally connected to a box at rest over the ledge, labeled m2. If m1 and m2 are a height h above the ground and m2>>m1: (a) What is the initial gravitational potential energy of the system? (b) What is the final kinetic energy of the system?

Answer 1

(a) The initial gravitational potential energy of the system is 0.5 (m₁ + m₂)gL.

(b) The final kinetic energy of the system is 0.5 (m₁ + m₂)gL .

Initial gravitational potential energy of the system

P.E = mgh

where;

• h is height of the incline

Let the length of the incline = L

h = L sinθ

P.E = mg(L sinθ)

P.E = (m₁ + m₂)g (L sinθ)

P.E = 0.5 (m₁ + m₂)gL

Final kinetic energy of the system

The final kinetic energy of the system is equal to the initial potential energy since the inclined plane is frictionless.

K.E(f) =  (m₁ + m₂)g (L sin30)

K.E(f) = 0.5 (m₁ + m₂)gL

Thus, the initial gravitational potential energy of the system is 0.5 (m₁ + m₂)gL and the final kinetic energy of the system is0.5 (m₁ + m₂)gL .

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