Question

if a force of 10 n acts on a mass of 5 kg producing an acceleration of 1.5 m/s², then what is the magnitude of the force of friction acting on the mass?
a. 10 n
b. 7.5 n
c. 5 n
d. 2.5 n

Explanation:

Step1: Apply Newton's second - law

According to Newton's second - law $F = ma$, where $F$ is the net force, $m$ is the mass and $a$ is the acceleration. The net force $F_{net}$ acting on the mass is related to the applied force $F_{applied}$ and the frictional force $F_f$ by $F_{net}=F_{applied}-F_f$. Also, $F_{net}=ma$.
We know that $F_{applied} = 10\ N$, $m = 5\ kg$ and $a=1.5\ m/s^{2}$.
First, find the net force using $F_{net}=ma$.
$F_{net}=5\times1.5 = 7.5\ N$.

Step2: Calculate the frictional force

Since $F_{net}=F_{applied}-F_f$, we can re - arrange the formula to find $F_f$.
$F_f=F_{applied}-F_{net}$.
Substitute $F_{applied} = 10\ N$ and $F_{net}=7.5\ N$ into the formula.
$F_f = 10 - 7.5=2.5\ N$.

Answer:

d. $2.5\ N$