Question

3 of 23 danielle just moved into a new apartment and her couch was left by the entrance. the couch has a mass of 115 kg and wood feet. the entrance into the apartment has a smooth hardwood floor while the living room is carpeted (see following chart for coefficients of friction). danielle initially tried pushing it by herself with a force of 180 n. then her brother, ramone, dropped by and helped. together they were able to push the couch where she wanted it in the living room. about how hard is the floor pushing up on the couch? a 10n b 1000n

Explanation:

Step1: Identify the force - equilibrium in vertical direction

In the vertical direction, the normal force $F_N$ (the force with which the floor pushes up on the couch) balances the gravitational force $F_g$. The gravitational force is given by $F_g = mg$, where $m$ is the mass of the couch and $g$ is the acceleration due to gravity ($g\approx9.8\ m/s^2$).

Step2: Calculate the gravitational force

$m = 115\ kg$, $g\approx9.8\ m/s^2$. Using the formula $F_g=mg$, we have $F_g=115\times9.8 = 1127\ N$. The normal force $F_N$ is approximately equal to the gravitational force in magnitude since the couch is in vertical - equilibrium. Among the given options, 1000 N is the closest.

Answer:

B. 1000N