Question

Carefully consider how the accelerations a1 and a2 are related. Solve for the magnitude of the acceleration, a1, of the block of mass m1, in meters per square second.

Answer 1

Answer:

a1 = 3.68m/s²

Explanation:

Given values:

Mass of the block placed on the table, m1 = 12.25 kg

Mass of the block hanging vertically, m2 = 7.5 kg

Acceleration due to gravity, g = 9.8 m/s2

Tension in the string is T

Let the acceleration of mass 1 and mass 2 be a1 and a2

a1 and a2 are equal in magnitude but different in direction. This because the string does not stretch. Hence the two bodies must move equal distances in equal times, and so their speechless at any instant must be equal. When the speeds change , they change by equal amounts in a given time, so the acceleration of the two bodies must have the same magnitude a,

a = m2*g/(m1 + m2)

a = 7.5 x 9.8 / (12.5 + 7.5)

a = 3.68 m/s²

a1 = a2 = 3.68m/s²

a1 is directed to the right and a2 is directed downwards

Below is a diamonds to show the geometrical arrangements of both masses