How Does Force Affect the Center of Mass and Momentum?

[TwinGemini14]

1. Ball 1, ball 2, and ball 3 have masses 1 kg, 2 kg, and 3 kg respectively, and are initially arranged at x = 5 m, x = 10 m, and x = 15 m respectively (see picture). y = 5 m for all three balls. Now suppose that a net force of 1 N is applied to ball 1 in the +y direction and a net force of 2 N is applied to ball 2 in the -y direction. The net force on ball 3 is zero.


What is the magnitude of the acceleration of the center of mass of the three-ball system?

A) 0.00 m/s2
B) 0.17 m/s2
C) 0.33 m/s2
D) 1.00 m/s2
E) 1.33 m/s2

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So I first drew out the picture of the masses. Since the net force on the system is 1N downward, I did...
1N / (m1+m2+m3) = 1/6 = 0.16666. So the answer is B?

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A block of mass 50 kg is sliding along in the +x direction (to the right) with initial magnitude of momentum p0 = 2450 kg*m/s on a horizontal frictionless surface.


Then a constant force F = 14 N is applied as shown in the above drawing, where the angle of the force above horizontal is 20°.

2) One second after the force is applied, the momentum of the block in the ground frame will have:

A) decreased in magnitude
B) been conserved
C) increased in magnitude

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The momentum has increased in magnitude since the object is accelerating due to a net force, correct? C?
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3) After the force is applied, the total mechanical energy of the block will:

A) be less than it was before the force was applied
B) remain the same as it was before the force was applied
C) be greater than it was before the force was applied

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C. Since the kinetic energy is gradually increasing due to a constant acceleration given by the applied force, the total mechanical energy is increasing.
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I already submitted this to a previous forum but reworked the problems. Does anybody see anything wrong with these? Thanks in advance.

 

[Kurdt]

The first looks ok to me. The second two are harder to tell without the diagram but they seem reasonable.

 

[nlightner]

I would like to provide a response to the given content by first acknowledging that these are well-defined problems and you have made an effort to solve them. However, I would like to offer some clarifications and corrections to your solutions.

In the first problem, you correctly calculated the net force on the system as 1N downward. However, the magnitude of the acceleration of the center of mass is not equal to the net force divided by the total mass of the system. Instead, it is equal to the net force divided by the total mass of the system, which in this case is 6 kg. Therefore, the correct answer is C) 0.33 m/s^2.

In the second problem, you correctly identified that the momentum of the block will increase in magnitude after the force is applied. However, it is important to note that the momentum will not only increase in magnitude but also change in direction due to the applied force at an angle. Therefore, the correct answer is C) increased in magnitude and direction.

In the third problem, you correctly identified that the total mechanical energy of the block will increase after the force is applied. However, it is important to note that the total mechanical energy is the sum of both kinetic and potential energy. Since there is no change in potential energy in this scenario, the total mechanical energy will be solely determined by the change in kinetic energy, which is increasing due to the applied force. Therefore, the correct answer is C) be greater than it was before the force was applied.

I hope this helps clarify any confusion and further your understanding of momentum and center of mass. Keep up the good work in your scientific studies!