Ablock of ice with mass 2 kg slides 0.750 m down an inclined plane that slopes downward at an angle of 36.9◦ below the horizontal. if the block of ice starts from rest, what is it’s final speed? you can ignore friction. work this problem two ways: with the work-energy theorem and using conservation of energy.

The final speed of the block is 2.97 m/s

Solution:

As per the question:

mass of the ice block, m = 2 kg

distance, d = 0.750 m

Angle,

Now,

We know that the work done can be given as the change in Kinetic energy of the block:

Since, the bock slides we have velocity in the downward direction only along the slope:

Now, the normal force is perpendicular to the displacement of the block, thus does not contribute to the work done, the only component of force that provides the work done is along the plane in the direction the block slides, thus:

Now, by work energy theorem:

Work done, W = Kinetic energy, KE

Thus