Inelastic Collision and Pendulums

• seichan
In summary, the problem asks to find the height the center of mass rises after the collision between two 23-cm long pendulums with masses of 0.145 kg and 0.200 kg, respectively, when the first pendulum is released from a height of 0.092 m and strikes the second pendulum, assuming a completely inelastic collision.
seichan

Homework Statement

Two 23-cm long pendulums (each made of a massless string and a ball) are initially situated as shown in the figure. The masses of the left and right balls are m1= .145 kg and m2= .200 kg , respectively. The first pendulum is released from a height d= .092 m and strikes the second. Assuming that the collision is completely inelastic and neglecting the mass of the strings and any frictional effects, how high does the center of mass rises after the collision?

U(x)=mgh
KE=1/2mv^2

The Attempt at a Solution

I started out by solving for the velocity of mass one when it strikes mass two. Because it is raised to a height d, its potential energy is mgd. Because energy is conserved, this is equal to the kinetic energy at its equilibrium point (where mass two is at rest). Thus, m1gd=.5m1V^2
sqrt(2gd)=V
I then used this velocity to calculate the Kinetic energy of mass two.
.5m2V^2=KE
.5m2(2gd)=KE
m2gd=KE
This, in turn, is equal to the potential energy at the height it goes to. Thus:
m2gh=m2gd
h=d

This, however is not the case (clearly). Whatever you could tell me about where my thinking has gone wrong would be greatly appreciated.

seichan said:
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The Attempt at a Solution

I started out by solving for the velocity of mass one when it strikes mass two. Because it is raised to a height d, its potential energy is mgd. Because energy is conserved, this is equal to the kinetic energy at its equilibrium point (where mass two is at rest).

It is mentioned explicitly that the collision is completely inelastic. In such collisions, mechanical energy is not conserved, and the two objects stick together. But the momentum of the system just before collision is equal to the momentum just afterward. From that you can find the speed just after impact.

Try it now.

The problem says that the collision is completely inelastic. This means that the bodies stick together after the collision. This means that V of m1 is NOT equal V of m2 after the collision. Use conservation of momentum to find the velocity of the combined mass after the collision and then figure how high it goes.

1. What is an inelastic collision?

An inelastic collision is a type of collision in which the kinetic energy of the system is not conserved. This means that some of the initial kinetic energy of the objects involved in the collision is lost, usually in the form of heat, sound, or deformation of the objects.

2. How is the momentum conserved in an inelastic collision?

In an inelastic collision, the total momentum of the system is still conserved, even though the kinetic energy is not. This means that the total mass and velocity of the objects before and after the collision will be the same.

3. How does a pendulum work?

A pendulum is a simple machine that consists of a weight (or bob) suspended from a fixed point by a string or rod. When the pendulum is pulled to one side and released, it swings back and forth due to the force of gravity and the tension in the string or rod. The motion of the pendulum is governed by the laws of physics, specifically the conservation of energy and the law of inertia.

4. What factors affect the period of a pendulum?

The period of a pendulum (the time it takes for one complete swing) is affected by the length of the pendulum, the mass of the bob, and the acceleration due to gravity. It is also affected by air resistance and the amplitude (or maximum displacement) of the swing, but these factors are usually negligible for simple pendulums.

5. How does the mass of the bob affect the period of a pendulum?

The mass of the bob does not affect the period of a pendulum. This is known as the "isochronous property" of a pendulum, meaning that the period remains the same regardless of the mass as long as the length and acceleration due to gravity stay constant.

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