Total mass of a system consisting of several particles 10 kg. To apply...
Total mass of a system consisting of several particles 10 kg. To apply...
Newton's Law of Motion in Centroidal Frame
To solve this problem, we need to understand Newton's law of motion and the concept of a centroidal frame.
Newton's Law of Motion:
Newton's law of motion states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. Mathematically, it can be represented as:
F = ma
Where F is the net force, m is the mass of the object, and a is the acceleration.
Centroidal Frame:
The centroidal frame is a reference frame in which the net external force acting on a system of particles is zero. In this frame, the system of particles appears to be at rest or moving with a constant velocity.
Calculating the Net External Force:
Given:
- Total mass of the system (m_total) = 10 kg
- Pseudo force acting on a particle (F_pseudo) = (4i - 2j) N
- Mass of the particle (m_particle) = 2 kg
To calculate the net external force acting on the whole system, we need to consider the pseudo force acting on the particle and the other forces acting on the system.
We know that the net force acting on the whole system is equal to the sum of all the forces acting on the individual particles of the system.
Calculating the Net External Force in x-direction:
The x-component of the net external force is given by:
F_net,x = F_particle,x + F_pseudo,x
Where F_particle,x is the force acting on the particle in the x-direction.
Since we are assuming that the particle is experiencing a pseudo force, the actual force acting on the particle in the x-direction will be:
F_particle,x = 0
Therefore, the x-component of the net external force is:
F_net,x = 0 + (4i - 2j)i = 4i
Calculating the Net External Force in y-direction:
The y-component of the net external force is given by:
F_net,y = F_particle,y + F_pseudo,y
Where F_particle,y is the force acting on the particle in the y-direction.
Since we are assuming that the particle is experiencing a pseudo force, the actual force acting on the particle in the y-direction will be:
F_particle,y = 0
Therefore, the y-component of the net external force is:
F_net,y = 0 + (4i - 2j)j = -2j
Calculating the Net External Force:
The net external force acting on the whole system can be calculated by combining the x and y components:
F_net = F_net,x + F_net,y = 4i - 2j
Final Answer:
Therefore, the net external force acting on the whole system is (4i - 2j) N, which corresponds to option (2) (-10i 20j) N.
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