Question

1. ella needs to move a 52 kg armoire across the room. she puts some cardboard under the feet of the armoire. find the coefficient of kinetic friction of the cardboard over the carpet, given that ella pushes with a force of 37 n, and the armoire accelerates at 0.19 m/s^2 (write your f_net equation for your free - body diagram)

Explanation:

Step1: Apply Newton's second - law

$F_{net}=ma$. The net - force in the horizontal direction is $F - f = ma$, where $F = 37N$ is the applied force, $f$ is the frictional force, $m = 52kg$ is the mass, and $a=0.19m/s^{2}$ is the acceleration.

Step2: Express the frictional force

The frictional force $f=\mu_{k}N$, and on a horizontal surface $N = mg$ (where $g = 9.8m/s^{2}$). So $F-\mu_{k}mg=ma$.

Step3: Solve for the coefficient of kinetic friction $\mu_{k}$

Rearrange the equation $F-\mu_{k}mg=ma$ to get $\mu_{k}=\frac{F - ma}{mg}$.
Substitute $F = 37N$, $m = 52kg$, $a = 0.19m/s^{2}$, and $g = 9.8m/s^{2}$ into the formula:
\[

$$\begin{align*} \mu_{k}&=\frac{37-(52\times0.19)}{52\times9.8}\\ &=\frac{37 - 9.88}{509.6}\\ &=\frac{27.12}{509.6}\\ &\approx0.05 \end{align*}$$

\]

Answer:

D. 0.05