A 1.0-kg mass is acted on by a net force of 4.0 N and a 3.0-kg mass is acted on by a net force of 3.0 N,in the directions shown.The acceleration of the center of mass of this system is approximately A)1.3 m/s²,53º N of E B)1.8 m/s²,45º N of E C)4.0 m/s²,due north D)5.0 m/s²,N of E E)7.0 m/s²,53º N of E

Question

Quizplus · Accepted Answer

The acceleration of the center of mass of a system can be calculated using the equation:
a = F_net / M_total
where F_net is the net force acting on the system and M_total is the total mass of the system.
For the first mass of 1.0 kg:
a_1 = F_net / M_1 = 4.0 N / 1.0 kg = 4.0 m/s^2
For the second mass of 3.0 kg:
a_2 = F_net / M_2 = 3.0 N / 3.0 kg = 1.0 m/s^2
The acceleration of the center of mass of the system can be found using the equation:
a_cm = (m_1 * a_1 + m_2 * a_2) / M_total
where m_1 and m_2 are the masses and M_total is the total mass of the system. 
Substituting the values, we get:
a_cm = (1.0 kg * 4.0 m/s^2 + 3.0 kg * 1.0 m/s^2) / (1.0 kg + 3.0 kg) 
a_cm = 2.0 m/s^2
The direction of the acceleration of the center of mass is not given, so it is not necessary to choose an answer option that matches a specific direction. Therefore, the best choice is (A) 1.3 m/s^2.

A 10-Kg Mass Is Acted on by a Net Force of of 4.0