# Momentum and Center of Mass

#### 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

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

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