3. If The Particles In A System All Move Together,
According to the laws of motion and rotational motion, the acceleration of an object's center of mass is equal to the total force acting on the system, and is calculated by dividing the sum of momentums by the total mass. This acceleration also applies to objects in uniform circular motion and always points towards the center of rotation. The forces acting on a system cause particles to move towards the center of mass, with the individual pieces having different accelerations. For the center of mass to not accelerate, the net force on the system must be zero, and a force must be applied to the system to maintain a constant speed. Acceleration, like velocity, has both magnitude and direction, and can be visualized as a vector.
Due to the external forces acting on the three-particle system, the center of mass of the system will accelerate. To find the acceleration of the center of mass, we can use the following formula:
[ \text{Acceleration of center of mass} = \frac{\sum m_i \cdot a_i}{\sum m_i} ]
Where:
- (m_i) = mass of each particle
- (a_i) = acceleration of each particle
Given the external forces F1 = 6.0 N, F2 = 12 N, and F3 = 14 N, the corresponding accelerations for the three particles can be found using Newton's second law: [ F = ma ] [ a = \frac{F}{m} ]
Using the acceleration of each particle, one can calculate the acceleration of the center of mass using the formula mentioned above. The direction of this acceleration will depend on the individual accelerations and the masses of the particles in the system.
For the specific calculation based on the provided external forces and masses, I'd need the masses of the particles to proceed with the numerical calculation.
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