PHY Book problems that im trying to figure out to do better on the test?

Question

Book problems that im trying to figure out to do better on the test


1. Particle A is located at the origin, particle B at the point (x, y) = (25 cm, 0). What is the location of the center of mass?
xcm
ycm

2. If a particle of mass 4.8 kg is moving east at 10 m/s and a particle of mass 16 kg is moving west at 10 m/s, what is the velocity of the center of mass of the pair?

3. Two identical gliders on an air track are held together by a piece of string, compressing a spring between the gliders. While they are moving to the right at a common speed of 0.52 m/s, someone holds a match under the string and burns it, letting the spring force the gliders apart. One glider is then observed to be moving to the right at 1.30 m/s.
What velocity does the other glider have?
___ m/s to the left.

Answer 1

1.

Let „a“ is the mass of particle A and „b“ is the mass of particle B.

Then the coordinates of the center of mass are
[b/(a+b)]*25 cm
and
0 cm.

2.

Let east is positive direction and west is negative direction.

The total weight of both particles is 20.8 kg.

The velocity of the center of mass is (4.8/20.8)*10 m/s – (16/20.8)*10 m/s = - 5.38 m/s.

3.

Let to the right is positive direction and to the left is negative direction.

The velocity of the center of mass of both gliders remains 0.52 m/s.

The center of mass is in the half of the distance between gliders because gliders are identical.

The velocity of one glider relative to the center of mass is 1.30 – 0.52 = 0.78 m/s.

The velocity of the other glider relative to the center of mass must be - 0.78 m/s.

Therefore the velocity of the other glider is 0.52 - 0.78 = - 0.26 m/s.

-

Answer 2

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