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 39 kg, the acceleration of the object is 2 m/s². when the same force acts upon another object, its acceleration is 13 m/s². what is the mass of this object?

Explanation:

Step1: Find the force

Since \(F = ma\) (Newton's second law), for the first object with \(m_1=39\space kg\) and \(a_1 = 2\space m/s^{2}\), the force \(F=m_1a_1\).
\(F=39\times2=78\space N\)

Step2: Find the mass of the second object

For the second object, \(F = 78\space N\) and \(a_2=13\space m/s^{2}\). Using \(F = ma\) (re - arranged as \(m=\frac{F}{a}\)), we substitute \(F = 78\space N\) and \(a=a_2\).
\(m=\frac{78}{13}=6\space kg\)

Answer:

\(6\space kg\)