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.
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.
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.
Expert Solution & Answer
To determine
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, F3=2N in the right direction.
b) Force acting on third particle when center of mass is moving rightward with constant velocity, F=2N in the right direction.
c) Force acting on third particle when center of mass is accelerating rightward, F3>2N in the right direction
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:
FNet=∑F
3) Given:
i) F1=5N acting on particle 1 in the left direction
ii) F2=3N acting on particle 2 in the right direction
4) Calculation:
a) For the center of mass to be stationary, the net force acting on the system should be equal to zero.
FNet=∑F=0
FNet=-5+3+F3=0
F3=2N
So, F3=2N and the positive sign indicates that it should be in the right direction.
b) For the center of mass to move on the right with constant velocity, net force acting on the system should be zero.
FNet=∑F=0
FNet=-5+3+F3=0
F3=2N
So, F3=2N and positive sign indicates that it should be in right direction.
c) For the center of mass to move in the right hand direction with some acceleration
FNet=∑F>0
FNet=-5+3+F3>0
F3>2N in right direction.
So, for center of mass to accelerate rightward, we should have F3>2N in the right direction
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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A 2.00 kg particle has the xy coordinates (1.20 m, 0.500 m), and a 4.00 kg particle has the xy coordinates (0.600 m, 0.750 m). Both lie on a horizontal plane. At what (a) x and (b) y coordinates must you place a 3.00 kg particle such that the center of mass of the three-particle system has the coordinates (0.500 m,0.700 m)?
An object with mass m1 = 3.00 kg is moving along the positive x axis with a speed v1i = 2 m/s straight towards two objects with masses m2 = 2.00 kg and m3 = 4.00 kg, which are initially at rest. When they collide, object 1 comes to rest and object 2 moves away with a speed of v2f = 1.5 m/s at an angle of 50 degrees above the x axis. What is the direction of the velocity of the center of mass of the system comprised of all three objects after the collision?
A) Along the x axis
B) A an angle of 50 degrees above the x axis
C) At an angle of 50 degrees below the x axis
D) At an angle > 0 degrees and <50 degrees above the x axis
E) At an angle>0 degrees and <50 degrees below the x axis
The correct answer is A but I am confused why it is A, if you could explain the justification as to why the answer is option A.
PART 1: A 5.00 kg particle has the xy coordinates (1.20 m, 2.00 m), and a 6.00 kg particle has the xy coordi-nates (0.300 m, 0.750 m). Both lie on a horizontal plane. At what (a) x and (b) y coordinates must you placea 4.00 kg particle such that the center of mass of the three-particle system has the coordinates (0.500 m, 0.900 m)?
PART 2: A rope is used to pull a 3.5 kg block at constant speed 6 m along a horizontal oor. The force onthe block from the rope is 7 N and directed = 20 above the horizontal. What are (a) the work done by therope's force, (b) the increase in thermal energy of the block- oor system. PART 3: Draw a labelled gure to explain the idea of turning point in terms of energy.
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