Question

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. which free - body diagram best represents the forces on the couch while it is being pushed along the floor at a constant speed?

Explanation:

Step1: Analyze forces on couch

When the couch is moving at a constant speed, the net - force on it is zero. There is the gravitational force ($F_{gravity}$) acting downwards, the normal force ($F_{norm}$) acting upwards, the applied force ($F_{push}$) in the direction of motion, and the frictional force ($F_{friction}$) opposite to the direction of motion.

Step2: Check force balance

Since the vertical forces balance ($F_{norm}=F_{gravity}$, where $F_{gravity} = mg$ with $m = 115$ kg and $g=9.8$ m/s²), and the horizontal forces balance ($F_{push}=F_{friction}$ for constant - speed motion).

Answer:

The free - body diagram with a downward arrow for $F_{gravity}$, an upward arrow for $F_{norm}$ of equal length, a right - ward arrow for $F_{push}$ and a left - ward arrow for $F_{friction}$ of equal length best represents the forces on the couch while it is being pushed along the floor at a constant speed.