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 = (F)/(m) \rightarrow 1^(st) Object`

For the second object the acceleration is,

`8a = (3F)/(m_2) \rightarrow 2^(nd) Object`

Solving for the mass of the second object,

`m_2 = (3F)/(8a)`

`m_2 = (3F)/(8(F/m))`

`m_2 = (3)/(8)m`

Therefore the correct answer is D.