# Collision (kinetic energy lost)

1. Apr 9, 2005

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 lets 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: Apr 10, 2005
2. Apr 10, 2005

### Staff: Mentor

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.

3. Apr 10, 2005

### HallsofIvy

Staff Emeritus
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!

4. Apr 10, 2005

### jdavel

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?

5. Apr 10, 2005

### Staff: Mentor

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.

6. Apr 11, 2005