Question

A net force of $10N$ gives an object an acceleration of $5m{s^{ - 2}}$ What net force would give the same object an acceleration of $8m{s^{ - 2}}?$.

Answer 1

Hint: In order to solve this question, we will first calculate the mass of a given object using Newton’s second law of motion mathematical formula and then again using the value of mass and acceleration we will use the same formula to find the force for a given situation.

Formula used:
According to Newton’s second law of motion, force applied on a body is equal to the product between mass of the body and acceleration produced in the body due to applied force. Mathematically, $F = ma$ where,
F is force applied on the body.
m is the mass of the body.
a is acceleration produced in the body.

Complete step by step solution:
According to the question, the force of $F = 10N$ causes an acceleration of $a = 5m{s^{ - 2}}$ in an object. Let ‘m’ be the mass of the object so, by using the formula $F = ma$ and on putting the value of parameters we get,
$10 = 5m$
$ \Rightarrow m = 2kg$
Hence, the mass of the object is $m = 2kg$ now in second case, Let F’ be the force required to move this object of mass $m = 2kg$ with an acceleration of $a' = 8m{s^{ - 2}}$ so putting the values of parameters we get,
$F' = ma'$
$F' = 2 \times 8$
$F' = 16N$
Hence, the force required to move the object with an acceleration of $a' = 8m{s^{ - 2}}$ is $F' = 16N$.

Note:
It should be remembered that, an object may be subjected to many forces in different directions but we always have to calculate the net force acting on a body and then use Newton's second law of motion formula to calculate either force, mass and acceleration of the body when other two parameters are given.