Question 16 (5 points)
Two objects rest on a uniform surface. A person pushes both with equal force. If the first object
starts to move faster than the second, what can be said about their masses?
The mass of the first object is less than that of the second object.
The mass of the first object is equal to the mass of the second object
The mass of the first object is greater than that of the second object
No inference can be made because mass and force are not related to each other

Question

UpStudy AI · Accepted Answer

Let the force applied on each object be $$ F $$.

According to Newton's second law, the acceleration $$ a $$ of an object is given by:
$$
a = \frac{F}{m}
$$
Let the masses of the first and second objects be $$ m_1 $$ and $$ m_2 $$, and their corresponding accelerations be $$ a_1 $$ and $$ a_2 $$.

Given that:
$$
a_1 > a_2
$$

Substitute the accelerations:
$$
\frac{F}{m_1} > \frac{F}{m_2}
$$

Since $$ F $$ is the same positive constant for both objects, dividing both sides by $$ F $$ gives:
$$
\frac{1}{m_1} > \frac{1}{m_2}
$$

This inequality implies:
$$
m_1 < m_2
$$

Thus, the mass of the first object is less than the mass of the second object.
The mass of the first object is less than that of the second object.

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