Question

a system consists of three discrete masses, and a different rightward force is exerted on each mass. a 2 n force is exerted on the 2 kg mass, a 16 n force is exerted on the 4 kg mass, and a 42 n force is exerted on the 6 kg mass as shown in the figure. what is the magnitude of the acceleration of the center of mass of the system?
(a) 1.0 m/s²
(b) 4.0 m/s²
(c) 5.0 m/s²
(d) 12.0 m/s²

Explanation:

Step1: Calculate total force

The total force $F_{total}$ is the sum of the individual forces. So $F_{total}=2 + 16+42=60\ N$.

Step2: Calculate total mass

The total mass $m_{total}$ is the sum of the individual masses. So $m_{total}=2 + 4+6 = 12\ kg$.

Step3: Use Newton's second - law for center of mass

According to Newton's second - law $F = ma$, for the center of mass $a_{cm}=\frac{F_{total}}{m_{total}}$. Substituting the values, we get $a_{cm}=\frac{60}{12}=5.0\ m/s^{2}$.

Answer:

C. $5.0\ m/s^{2}$