Question

If a force of 50 N is exerted on two objects, one with a mass of 14.0 kg and the other with a mass of 41.0 kg, which object will have the greater acceleration?

Answer 1

Recall Newton's 2nd law of motion

`\begin{gathered} F=m\cdot a \\ a=(F)/(m) \end{gathered}`

The above equation means that the acceleration of an object is dependent upon the net force acting upon the object and the mass of the object.

The acceleration is directly proportional to the net force acting upon the object.

The acceleration is inversely proportional to the mass of the object.

For the given case, the net force acting upon both the objects is the same that is 50 N.

So, the mass of the objects will determine which object will have the greater acceleration.

`\begin{gathered} a_1=(F)/(m_1)=(50)/(14.0)=3.57\; \; (m)/(s^2) \\ a_2=(F)/(m_2)=(50)/(41.0)=1.22\; \; (m)/(s^2) \end{gathered}`

As expected, the acceleration of the object is greater for the object having a smaller mass.

Therefore, the object with a mass of 14.0 kg has a greater acceleration (3.57 m/s^2)