Question

Take 2 (or is it 3) on this question. Box a (ma = 2kg) is on a table with some friction ( = 0.4). Box b (mb = 5kg) is hanging over the side of the table. Using energy, how fast is box b going when it hits the ground if box b starts 1.75m above the ground? Only now the solid pulley has to be taken into account. The pulley is solid and has a mass of 0.75kg and a diameter of 20cm.

I have seen an answers for this question posted but it's just the answer and doesn't go trough the equations.

Answer 1

The initial energy of the system (when everything at rest, only potential energy comes into the play)

Now, as the box on the table moves the same distance on the table, the work done by the friction on the box is

The moment of inertia of the pully is

The final energy of the system (when (or just before) the box hits the surface, the potential energy is zero, so, only kinetic energy comes into play)

Putting the values

Now, from work energy theorem

So, when the box hits the ground, its velocity is 4.42 m/s.