Question

when a constant force is applied to an object, the acceleration of the object varies Inversely with its mass. When a certain constant force acts upon an object with mass 22 kg, the acceleration of the object is 2 m/s². When the same force acts upon another object, its acceleration is 11 m/s? What is the mass of this object? ​

Answer 1

Answer:

The mass of the object is 4 kilograms.

Explanation:

From the Second Newton's Law, under the same force, we know that the mass of the object is inversely proportional to the acceleration experimented by the object:

$m_{1}\cdot a_{1} = m_{2}\cdot a_{2}$ (1)

Where:

$m_{1}$, $m_{2}$ - Masses, in kilograms.

$a_{1}, a_{2}$ - Accelerations, in meters per square second.

If we know that $m_{1} = 22\,kg$, $a_{1} = 2\,\frac{m}{s^{2}}$ and $a_{2} = 11\,\frac{m}{s^{2}}$, then the resulting mass is:

$m_{2} = m_{1} \cdot \left(\frac{a_{1}}{a_{2}} \right)$

$m_{2} = (22\,kg)\cdot \left(\frac{2\,\frac{m}{s^{2}} }{11\,\frac{m}{s^{2}} } \right)$

$m_{2} = 4\,kg$

The mass of the object is 4 kilograms.