Question

question 4 of 10 dale and alex push on opposite sides of a couch. dale pushes to the left with a force of 100 n, while alex pushes to the right with a force of 175 n. if the couch has a mass of 55 kg, what is the acceleration of the couch? a. 5 m/s² left b. 1.4 m/s² left c. 1.4 m/s² right d. 5 m/s² right

Explanation:

Step1: Calculate net - force

The forces are in opposite directions. Let the right - direction be positive. The net force $F_{net}=F_{Alex}-F_{Dale}$. Given $F_{Dale} = 100N$ (left, so negative) and $F_{Alex}=175N$ (right, so positive). Then $F_{net}=175 - 100=75N$ (positive, so to the right).

Step2: Use Newton's second law

Newton's second law is $F = ma$, where $F$ is the net force, $m$ is the mass, and $a$ is the acceleration. We know $F_{net}=75N$ and $m = 55kg$. Rearranging for $a$, we get $a=\frac{F_{net}}{m}$. Substituting the values, $a=\frac{75}{55}\approx1.4m/s^{2}$. Since the net force is positive, the acceleration is to the right.

Answer:

C. $1.4m/s^{2}$ right