Conservation of Momentum in a Two-Pendulum Collision

In summary, the problem involves two pendulums of different masses colliding and sticking together. After the collision, the maximum angle made by the support strings with respect to the vertical can be found using conservation of momentum. The answer is arccos [ [30 + sqrt(2)] / 32 ] = arccos [ 0.9817 ] = 79.0 degrees.
  • #1
Eternal Ophidian
1
0
I have to solve this problem but every answer I've come up with so far has been wrong. If anyone knows how to solve it, I'd greatly appreciate some enlightenment. Thanks.
Here's the question:
Two pendulums are hung adjacent to each other as shown in Fig. 7.20. Bob 1 has a mass m, and bob 2 has a mass 3m. Bob 1 is pulled aside until the support string makes an angle of 45° with the vertical direction and then is released. When the bobs collide, they stick together. What is the maximum angle made by the support strings with respect to the vertical after the collision?
 
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  • #2
is the answer

arccos [ [30 + sqrt(2)] / 32 ]
= arccos [ 0.9817 ]
= 79.0 degrees?
 
  • #3
In order to find the maximum angle that the two balls rise to, you need to know the velcoity of the two balls after the collision. This is easy to find using conservation of momentum
m1v1+m2v2=(m1+m2)v'
One of the balls is initially at rest, so the problem is even easier.
m1v1=(m1+m2)v'
 

FAQ: Conservation of Momentum in a Two-Pendulum Collision

What is a pendulum momentum problem?

A pendulum momentum problem is a physics problem that involves analyzing the motion of a pendulum, which is a weight suspended from a fixed point that swings back and forth under the influence of gravity.

What factors affect the momentum of a pendulum?

The factors that affect the momentum of a pendulum include the mass of the weight, the length of the string or rod it is suspended from, and the angle at which it is released. The force of gravity and air resistance may also play a role.

How is the momentum of a pendulum calculated?

The momentum of a pendulum can be calculated using the formula p = mv, where p is momentum, m is mass, and v is velocity. In a pendulum, the velocity is constantly changing as the pendulum swings back and forth, so the average velocity is typically used in calculations.

What is the difference between kinetic energy and momentum in a pendulum?

Kinetic energy is the energy an object possesses due to its motion. In a pendulum, kinetic energy is constantly changing as the pendulum swings back and forth. Momentum, on the other hand, is the product of an object's mass and velocity and is a measure of its motion. In a pendulum, momentum remains constant as long as there is no external force acting on it.

How does the length of a pendulum affect its momentum?

The length of a pendulum affects its momentum in that a longer pendulum will have a greater momentum than a shorter pendulum at the same angle of release. This is because the longer pendulum has a greater distance to travel and therefore a higher velocity, resulting in a higher momentum.

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