Question

A 100-N force causes an object to accelerate at 2 m/s/s. What is the mass of the object?

Answer 1

Answer:

$50\; \rm kg$.

Explanation:

By Newton's Second Law, the acceleration $a$ of an object is proportional to the net force $\sum F$ on it. In particular, if the mass of the object is $m$, then

$\sum F = m \cdot a$.

Rewrite this equation to obtain:

$\displaystyle m = \frac{\sum F}{a}$.

In this case, the assumption is that the $100\; \rm N$ force is the only force that is acting on the object. Hence, the net force $\sum F$ on the object would also be

Make sure that all values are in their standard units. Forces should be in Newtons (same as $\rm kg \cdot m \cdot s^{-2}$, and the acceleration of the object should be in meters-per-second-squared ($\rm m \cdot s^{-2}$). Apply the equation $\displaystyle m = \frac{\sum F}{a}$ to find the mass of the object.

$\displaystyle m = \frac{100\; \rm N}{2\; \rm m \cdot s^{-2}} = 50\; \rm kg$.