Question

A block of mass
m1 = 4.50 kg
initially at rest on top of a frictionless, horizontal table is attached by a lightweight string to a second block of mass
m2 = 2.70 kg
hanging vertically from the edge of the table and a distance
h = 0.410 m
above the floor (as shown in the figure below). If the edge of the table is assumed to be frictionless, what is the speed with which the first block leaves the edge of the table? (Assume the first block leaves the edge of the table after the second block reaches the floor.)

Answer 1

The speed with which the first block leaves the edge of the table is 2.84 m/s.

Conservation of mechanical energy

Since both blocks are connected, they will travel at the same speed from the given position. The potential energy of the blocks at the given position will be converted to kinetic energy.

P.E = K.E

mgh = ¹/₂mv²

gh = ¹/₂v²

$v = \sqrt{2gh}$

The speed of the blocks from the given position is calculated as follows;

$v = \sqrt{2 \times 9.8 \times 0.41} \\\\v = 2.84 \ m/s$

Thus, the speed with which the first block leaves the edge of the table is 2.84 m/s.

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