work and energy?

Question

a block of mass 2 kg is kept on a rough inclined plane of inclination 30 fixed in an elevator. the elevator starts to come down with an acceleration of 2ms and block remains at rest on the incline. whate is the work done by the normal force acting on the block in 4 second
answer 96 j

Answer 1

No work is done by the normal force as the block didn't move relative to the incline. work=force*distance
Zero distance along the force means no work done.

Answer 2

As the other answer said...no work. Hard to believe isn't it?

But work, as defined by the work function, is J = Fs; where F is a force acting over and in the direction of a distance s. As the block remains fixed on the plane, there is no work along the plane. Thus, there is no work against friction forces that depend on the Normal weight. But what about work along the direction of the elevator fall?

The net force on the block as the elevator drops is f = W - ma; where the m = 2 kg block mass and a = 2 m/sec^2 (not per sec as you show it). W = mg, the weight of the block; where g = 9.81 m/sec^2 at Earth's surface. Thus N = f cos(theta); where theta = 30 degrees.

As the normal force is not acting in the direction of the elevator fall, no work is being done by it. But, and this is a big BUT, there is a lot of work being done by f because that is acting over and in the direction of the fall.

If t = 4 sec, the lift falls s = 1/2 at^2 if the time and fall were begun with the elevator initially at rest. So J = fs = m(g - a) 1/2 at^2 is the work done by the fall of the elevator. You can do the math. But be aware, f is not the normal force; it's the net force acting on the block in the direction of the vertical fall of the elevator.

Answer 3

The mass of 2kg has fallen through a distance of (0.5 x 2 x 4^2) = 16 m down.

The work done by a force acting on it Force x distance = mah = 2 x 2 x 16 = 64 Joule.

By conservation of energy, the normal force also should have lost such energy.

The work done by the normal force is - 64 joule.

Your answer 96 is wrong. or the values for mass and acceleration may be wrong.
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