Question

Two forces, one four times as large as the other, pull in the same direction on a 10kg mass and impart to it an acceleration of 2.5 m/s2. If the smaller force is removed, what is the acceleration of the mass?

Answer 1

Answer:

The acceleration of the mass is 2 meters per square second.

Explanation:

By Newton's second law, we know that force ($F$), measured in newtons, is the product of mass ($m$), measured in kilograms, and net acceleration ($a$), measured in meters per square second. That is:

$F = m\cdot a$ (1)

The initial force applied in the mass is:

$F = (10\,kg)\cdot \left(2.5\,\frac{m}{s^{2}} \right)$

$F = 25\,N$

In addition, we know that force is directly proportional to acceleration. If the smaller force is removed, then the initial force is reduced to $\frac{4}{5}$ of the initial force. The acceleration of the mass is:

$\frac{25\,N}{20\,N} = \frac{2.5\,\frac{m}{s^{2}} }{a}$

$a = 2\,\frac{m}{s^{2}}$

The acceleration of the mass is 2 meters per square second.