Question

A force F produces an acceleration a on an object of mass m. A force 3F is exerted on a second object, and an acceleration 8a results. What is the mass of the second object in terms of m?
a. 3m
b. 9m
c. 24m
d. (3/8)m
e. (8/3)m

Answer 1

To solve this problem we will proceed to use Newton's second law for which the mass (m) multiplied by the acceleration (a) is defined as the Force (F) applied on a body, mathematically that is,

$F = ma$

According to the statement for the first object, the acceleration is,

$a = \frac{F}{m} \rightarrow 1^{st} Object$

For the second object the acceleration is,

$8a = \frac{3F}{m_2} \rightarrow 2^{nd} Object$

Solving for the mass of the second object,

$m_2 = \frac{3F}{8a}$

$m_2 = \frac{3F}{8(F/m)}$

$m_2 = \frac{3}{8}m$

Therefore the correct answer is D.