A block of mass m starts from position 1 and moves up a frictionless inclined plane with an initial speed v. At some later time the block has moved down the plane and at position 2 has a speed u. If a and b are the heights above the bottom of the plane, the magnitude of u can be determined from A) u² = v² - 2g(a - b) B) u² = v² + 2g(a + b) C) u² = v² + 2g(a - b) D) u² = v² + 2g(b - a) E) u² = v² + g(a - b)

Question

Quizplus · Accepted Answer

The conservation of energy principle can be applied to the motion of the block. The initial kinetic energy of the block equals the sum of the potential and kinetic energy when it reaches position 2. Using this principle, we can write:

1/2 mv^2 = mgh + 1/2 mu^2

where h = a - b is the height difference between positions 1 and 2.

Simplifying this equation, we get:

u^2 = v^2 + 2gh

Substituting h = a - b, we get:

u^2 = v^2 + 2g(a - b)

Taking the square root of both sides, we get:

u = sqrt(v^2 + 2g(a - b))

Therefore, the correct answer is C.

A Block of Mass M Starts from Position 1 and Moves