# At a construction site, a 22kg bucket of concrete is connected over a very light frictionless...

## Question:

At a construction site, a 22kg bucket of concrete is connected over a very light frictionless pulley to a 375N box on the roof of a building.

Assuming the roof is frictionless what is the magnitude of the acceleration of the bucket?

## Newton's Second Law

According to Newton's second law, the net force on an object is given by the product of mass and acceleration of the object. If the object is at rest then force on it would be zero.

Given

Mass of the bucket (m) = 22 kg

Mass of the box {eq}\displaystyle M = \dfrac{W}{g} \\ M = \dfrac{375}{9.81} = 38.23 \ kg {/eq}

Now, let us consider the tension in the string is "T", therefore

On applying Newton's second law on the box, we can write

{eq}\displaystyle T= Ma \\ T = 38.23a \ -------------(1) {/eq}

Where

• a is the acceleration of the system

Now, applying Newton's second law on the bucket

{eq}\displaystyle mg - T = ma \\ mg - Ma = ma \\ mg = (m+M)a \\ a(22+38.23) = 22*9.81 \\ a = 3.58 \ m/s^{2} {/eq}