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 f_net equation for your free body diagram)

Explanation:

Step1: Apply Newton's second - law

According to Newton's second - law $F_{net}=ma$. The net force acting on the armoire is $F - F_f=ma$, where $F$ is the applied force, $F_f$ is the frictional force, $m$ is the mass of the armoire, and $a$ is the acceleration. The frictional force $F_f=\mu_k N$, and on a horizontal surface $N = mg$ (where $g = 9.8\ m/s^2$). So $F-\mu_kmg=ma$.

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

We can rearrange the formula $F-\mu_kmg=ma$ to $\mu_k=\frac{F - ma}{mg}$.

Step3: Substitute the given values

Given $F = 37\ N$, $m = 52\ kg$, $a=0.19\ m/s^2$, and $g = 9.8\ m/s^2$.
First, calculate the numerator: $F - ma=37-52\times0.19=37 - 9.88 = 27.12$.
Then, calculate the denominator: $mg=52\times9.8 = 509.6$.
Finally, $\mu_k=\frac{27.12}{509.6}\approx0.05$.

Answer:

0.05