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/s² (write your fnet equation for your free - body diagram)

Explanation:

Step1: Apply Newton's second law

According to Newton's second law $F - f=ma$, where $F$ is the applied - force, $f$ is the frictional force, $m$ is the mass, and $a$ is the acceleration. The frictional force $f = \mu_kN$, and on a horizontal surface $N = mg$. So $F-\mu_kmg=ma$.

Step2: Rearrange the formula to solve for $\mu_k$

We can rewrite the equation $F-\mu_kmg = ma$ as $\mu_k=\frac{F - ma}{mg}$.
Given that $F = 37\ N$, $m = 52\ kg$, $a=0.19\ m/s^2$, and $g = 9.8\ m/s^2$.
Substitute the values 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:

0.05