How Do You Solve the Motion of Two Colliding Pendulums?

In summary, the problem involves two pendulums with different masses and periods, hanging from a common point. Using the period equation, the length of each pendulum can be calculated. To find the maximum speed of Pendulum A, the kinetic energy and potential energy equations can be used. Finally, the conservation of momentum formula can be applied to determine the mass of Pendulum B in the scenario where the two pendulums collide and one comes to a complete stop while the other moves backward with half of its original speed.
  • #1
mattwild
7
0
AP Physics HW Help -- Motion of 2 Pendulums

Homework Statement



A system consists of two metal balls hanging by strings of length L fixed at a common point as shown. Pendulum A has a mass of 2kg and Pendulum B has a period of 2.0s.

a. What is the length L of each pendulum?
b. What is the maximum speed Pendulum A reaches after being released from a height of 0.6m above its equilibrium position (neglect friction)
c. Pendulums A and B are released at the same time from the same height, colliding right in the middle of their arcs. If Pendulum A comes to a complete stop after the collision while Pendulum B moves backward with half of its original speed, what is the mass of Pendulum B>

Homework Equations



Period equations
Kinetic Energy Maybe?
Conservation of momentum

The Attempt at a Solution



For a. I used to formula Tp=2Pi(sqrrt of L/g)
For b. I have no clue maybe use something with KE and PE
For c. Conservation of momentum formula I am thinking?HERE IS THE DIAGRAM:

http://imgur.com/GK1ZvFf
 
Last edited:
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  • #2
You have all the right ideas - just use them.
 

1. How do I calculate the period of a pendulum?

The period of a pendulum can be calculated using the formula T = 2π√(l/g), where T is the period (in seconds), l is the length of the pendulum (in meters), and g is the acceleration due to gravity (9.8 m/s² on Earth).

2. What is the relationship between the length of a pendulum and its period?

The length of a pendulum and its period are directly proportional. This means that as the length of a pendulum increases, its period also increases. This relationship is described by the formula T = 2π√(l/g), where T is the period, l is the length, and g is the acceleration due to gravity.

3. How does the mass of a pendulum affect its motion?

The mass of a pendulum does not affect its motion. The period and frequency of a pendulum are dependent only on its length and the acceleration due to gravity. However, the mass of a pendulum can affect the amplitude of its motion, as a heavier mass will cause the pendulum to swing with a smaller amplitude.

4. What factors affect the period of a pendulum?

The period of a pendulum is affected by its length and the acceleration due to gravity. Other factors that can affect the period include air resistance, the angle at which the pendulum is released, and the amplitude of its swing.

5. How do I solve for the velocity of a pendulum?

The velocity of a pendulum can be calculated using the formula v = √(gl(1-cosθ)), where v is the velocity (in m/s), g is the acceleration due to gravity, l is the length of the pendulum, and θ is the angle at which the pendulum is released (measured from the vertical).

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