# Collision (kinetic energy lost)

In summary: I appreciate it!In summary, the two pendulums swing together at a maximum angle after the collision. Energy is lost during the collision, and the maximum angle is determined by the amount of kinetic energy lost.
Ok, I'm really lost here. I guess I do not understand the equations well enough to think on my own in this question :)

So the question is as follows:
Two simple pendulums of equal length are suspended from the same point. The pendulum bobs are point like masses. m1 > m2. The more massive bob (m1) is initially drawn back at an angle of 40^(degrees) from vertical. After m1 is released what is:

1. Find the speed of m1 just before the collision.
2. Determine the maximum angle to which the masses swing after the collision.
3. How much energy is lost during the collision?

Ok, I understand how to do 1 and 2. But I have no idea what to do with question 3.
To make things easier let's assume the folllowing variables have been derived or are known:
m1
m2
v_1i : initial velocity of pendulum swinging towards the stationary bob
v_1f : the velocity of the larger bob after the collision
v_2i : = 0... since the lower-mass-bob is not moving
v_2f : the velocity of the smaller bob after the collision

Any suggestion on how to handle the loss in kinetic energy would be fantastic... thank you.

Initial Kinetic Energy:
$$KE_i = \frac{1}{2}m_1(v_{1i})^2 + \frac{1}{2}m_2(0)^2$$

$$KE_f = \frac{1}{2}(v_{1f})^2 + \frac{1}{2}m_2(v_{2f})^2$$

So the loss of kinetic is $$KE_f - KE_i$$ ...? right? :)

Last edited:
So the loss of kinetic is $$KE_f - KE_i$$ ...? right? :)
That will be the change in KE, which is negative in this case. The loss of KE would be $$KE_i - KE_f$$. But you've got the idea.

Interesting. "Probasket" (any relation?) asked basically the same question except added that this a completely inelastic collision- that the to pendulum bobs move as one after the collision. Without that, there is no reason to think that any energy is lost!

How did you calculate v1f and v2f without knowing how much KE is lost? Aren't there an inifinite number of combinations of values for v1f and v2f that conserve momentum?

Right. FrogPad seems to have left out some key information in the statement of the problem (like the two masses stuck together after impact) that allowed him to solve parts 1 and 2.

Ahh yes, sorry about that. The question does not explicitly say that it is an inelastic collision, instead you have to make this assumption based off of:

2. Determine the maximum angle to which the masses swing after the collision.

Which I guess infers that the maximum angle of both objects "stuck together". I guess if it said: "determine the maximum angle's' then it would be an elastic collision.

Seriously though, thank you very much for the comments.

## 1. What is collision?

Collision is a physical event in which two or more objects come into contact with each other. This can result in a change in the motion or shape of the objects involved.

## 2. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is calculated by multiplying the mass of an object by its velocity squared.

## 3. How is kinetic energy lost in a collision?

Kinetic energy can be lost in a collision due to the transfer of energy between the colliding objects. Some of the kinetic energy is converted into other forms of energy, such as heat or sound.

## 4. What factors affect the amount of kinetic energy lost in a collision?

The amount of kinetic energy lost in a collision depends on the masses and velocities of the objects involved, as well as the elasticity of the collision. In an elastic collision, where there is no loss of kinetic energy, the objects bounce off each other. In an inelastic collision, some kinetic energy is lost as the objects stick together after impact.

## 5. How is the coefficient of restitution related to kinetic energy lost in a collision?

The coefficient of restitution is a measure of the elasticity of a collision. It is the ratio of the final velocity of separation to the initial velocity of approach. The lower the coefficient of restitution, the more kinetic energy is lost in the collision.

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