# Slider energy on rod

1. Feb 19, 2007

### stinlin

1. The problem statement, all variables and given/known data
Collar B has a mass of 4 kg and is attached to a spring of constant 1500 N/m and of undeformed length 0.4 m. The system is set in motion with r = 0.2 m, v_theta = 6 m/s, and v_r = 0. Neglecting the mass of the rod and the effect of friction, determine the radial and transverse components of the velocity of the collar when r = 0.5 m.

2. Relevant theories

Conservation of energy - kinetic and potential energy

3. The attempt at a solution

I used conservation of energy :

V_spring_initial = V_spring_final + T_slider_final

x_initial_spring = abs(0.2-0.4)
x_final_spring = abs(0.5-0.4)

I solved for v_r and got 3.35 m/s, which is NOT the right answer.

If I figure out how to solve for v_r, I'm still in the situation where I don't really know how to solve for v_theta. I'm thinking I can determine the force due to the spring and set that equal to m*a_normal, solve for v_theta there (because v^2 = (v_tangential)^2 = (v_theta)^2).

Can I get some help? Thanks a bunch!

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2. Feb 19, 2007

### Saketh

Use conservation of angular momentum to find the velocity in the tangential direction as a function of the radius.

Use a net force equation to find the velocity in the radial direction as a function of the radius. (You can consider it as an "inertial" frame with a fictional force, if you want.)

3. Feb 19, 2007

### stinlin

We haven't done angular momentum in class yet. While I do know it, he wants us to try and stick to the concepts we know.

4. Feb 20, 2007

### stinlin

Is there any more thoughts on this one or no??

5. Feb 20, 2007

### andrevdh

If one looks at just the SHM motion of the slider its energy stays constant throughout the motion:

$$\frac{1}{2}Ax^2$$

which enables one to calculate the radial velocity at any position.

Looking at the bigger picture the total mechanical energy (which will stay
constant since the slider is subject to a conservative force) of the slider should also include its rotational kinetic energy:

$$\frac{1}{2}I\omega ^2$$

, where its rotational velocity is determined by the tangential velocity.

Last edited: Feb 20, 2007
6. Feb 20, 2007

### stinlin

But the concept of moment of inertia hasn't been formally introduced in our class yet, so we can't really use that equation.

7. Feb 20, 2007

### cipotilla

How did you get the answer for Vr? What principle did you use? I was going to suggest you use the work-energy principle.

8. Feb 21, 2007

### andrevdh

Ok. You can then still use the fact that T + V will stay constant. The speed that you get will be the real speed of the slider, that is the tangential and radial speed combined or just v.