Figure 9-23 shows an overhead view of three particles on which external forces act. The magnitudes and directions of the forces on two of the particles are indicated. What are the magnitude and direction of the force acting on the third particle if the center of mass of the three-particle system is (a) stationary, (b) moving at a constant velocity rightward, and (c) accelerating rightward?
Figure 9-23 Question 1.
To find:
a) the force acting on third particle when center of mass is stationary.
b) the force acting on third particle when center of mass is moving rightward with constant velocity.
c) the force acting on third particle when center of mass is accelerating rightward.
Answer to Problem 1Q
Solution:
a) Force acting on third particle when center of mass is stationary,
b) Force acting on third particle when center of mass is moving rightward with constant velocity,
c) Force acting on third particle when center of mass is accelerating rightward,
Explanation of Solution
1) Concept:
We have to calculate the net force acting on the system.As the system contains three particles and the center of mass is to remain stationary, the net force acting on the system should be zero. Using this we can find the force acting on the third particle.
2) Formula:
3) Given:
i)
ii)
4) Calculation:
a) For the center of mass to be stationary, the net force acting on the system should be equal to zero.
So,
b) For the center of mass to move on the right with constant velocity, net force acting on the system should be zero.
So,
c) For the center of mass to move in the right hand direction with some acceleration
So, for center of mass to accelerate rightward, we should have
Conclusion:
Considering the direction and magnitude of the acceleration of the center of mass, we can find the direction and magnitude of the net force acting on the third particle.
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