6.1.3 The Center of Mass and the Motion of a System of Particles

Question 1

The Center of Mass and the Motion of a System of Particles

Answer 1

• Newton’s laws apply even to complicated objects as long as you think of them as point objects concentrated at their center of mass. This fact can be mathematically proven from the definition of the center of mass.
• The center of mass of an object can lie outside of the object.
• The center of mass of a system will always obey Newton’s laws, regardless of what may happen to the individual pieces of the system.

Question 2

Consider a bar of total mass 30 kg in which two-thirds of its mass is copper and the other third is iron. In addition, two 50-N weights are hanging from the ends of the bar, as shown in the diagram. Where would we tie a string around the bar in order to hang it up from the ceiling and keep it horizontal?

Answer 2

1.5 m

Question 3

True or false?

The center of mass is a point located within the object it describes.

Answer 3

false

Question 4

Which of the following coordinates is the center of mass for the object in the diagram? The mass is spread uniformly throughout the object.

Answer 4

(3, 2.3)

Question 5

A model rocket is launched off a cliff and flies along a parabolic path until it blows apart into four pieces of different masses. Which of the following diagrams best represents the path the center of mass of the four pieces will follow after the explosion?

Answer 5

-

Question 6

A group of five geese, each with mass m, are flying in their characteristic “V” formation. Each goose is flying at a speed of 10 m / s and its relative position shown in the diagram. Which of the following is the position and speed of the center of mass of the system of geese?

Answer 6

(2, 1.6) and 10 m / s

Question 7

A 1 kg mass is hung at the 0 mark of a meter stick and a 3 kg mass is hung at the 100 cm mark of the same meter stick. If the mass of the meter stick is 0.2 kg, at which of the following points of the meter stick could you balance the system on one finger?

Answer 7

73.8 cm

Question 8

Which of the following is the center of mass for the Earth-Moon system with respect to the Earth’s center? The mass of the Earth is 610^24 kg, the Earth’s radius is 6.410^6 m, the mass of the moon is 7.410^22 kg, and the radius of the moon is 1.710^6m, and the distance between the centers of the Moon and Earth is 3.8*10^8m.

Answer 8

4.63*10^6m

Question 9

True or false?
The location of the center of mass for the system of particles shown in the diagram is the origin of the coordinate system shown.

Answer 9

true

Question 10

A 16 kg projectile is fired from a cannon off a cliff. As it moves through a parabolic trajectory, it splits into a 6 kg piece and a 10 kg piece, as shown in the diagram. The 6 kg piece lands 30 meters from where the projectile would have landed if it had stayed intact. How far away from the 6 kg piece does the 10 kg piece land?

Answer 10

48 m