1. Apr 12, 2006

### skittlesj526

Can anyone help with one or more of these problems? I need them to study with for an exam by Thursday evening. Thank you in advance!

1. A .30-Kg object with a velocity if 0.60 m/s in the +x direction makes a head on elastic collision with a 0..40 Kg object initially at rest. What is the final velocity of the 0.30-Kg object after collision?

2. A railroad car, of mass 220Kg, rolls with no friction on a horizontal track with a speed of 15 m/s. A 80 Kg stunt man drops straight down a distance of 6.0 m, and lands in the car. How fast will the car be moving after this happens?

3.A small bomb, of mass 12 Kg, is moving toward the North with a velocity of 5.0 m/s. It explodes into three segments: a 6.0 Kg fragment moving west with a speed of 9.0 m/s; a 4.0 Kg fragment moving East with a speed of 10 m/s; and a third fragment with a mass of 1.0 Kg. What is the velocity of the third fragment? (neglect friction)

4. A pendulum of length 60cm is pulled 35cm away from the vertical axis and released with a speed of 2.0 m/s. What will be its speed at the bottom of the swing

2. Apr 12, 2006

### Staff: Mentor

Welcome to PF, skittles. You need to show your work so far on each of these problems in order to get help from us. What have you done so far on each of these problems? What equations are you going to use to work with these questions about acceleration, velocity and position?

3. Apr 13, 2006

### skittlesj526

Well, i do know that there is an elastic head-on collision which means change in momentum and conservation of KE.

4. Apr 13, 2006

### Hootenanny

Staff Emeritus
Can you form an expression based on those comments. HINT: In an elastic collision both, kinetic energy and momentum are conserved.

5. Apr 13, 2006

### skittlesj526

Well, i figured the first one out. I found the velocity of mass B prime and used it to find the velocity of mass A prime. I'm working on number 4 right now. I'm thinkin that total energy at point A is equal to total energy at point B but there is no mass or angle and I don't know how to determine the height for the PE equation unless I should be using a different equation, but which?

6. Apr 13, 2006

### Hootenanny

Staff Emeritus
You need to use trig to determine the change in height. As for the unknown mass, if you use the equations for potential and kinetic energy, you will find that the masses will cancel out.

Reagrds,
-Hoot

7. Apr 13, 2006

### skittlesj526

yeah i see that the masses will cancel out....but there is one problem....i've never had trig and don't know where to begin with a trig formula...is there a name?

8. Apr 13, 2006

### Hootenanny

Staff Emeritus
You've never done trigonometry? Sine, cosine, tangent etc?

9. Apr 13, 2006

### skittlesj526

yeah, SOH CAH TOA, right? but i don't even have an angle

10. Apr 13, 2006

### Hootenanny

Staff Emeritus
You can calculate an angle, in this case you have a triangle. At the maximum displacement the hypotenues is the string length, the base is the x displacement.

So you have;

$$\theta = \left( \frac{0.35}{0.6} \right) \cos^{-1}$$

You can then use either sine or tan to find the opposite side, which will then allow you to calculate the change in height. You may find it useful to draw a diagram.

Regards,
-Hoot

11. Apr 13, 2006

### skittlesj526

so now that i have the angle, i can set TEa=TEb. Does it start with PE and KE? so that....
TEa=PE+KE and TEb=KE ?

12. Apr 13, 2006

### Hootenanny

Staff Emeritus
Yes, it starts with both potential and kinetic energy. I'm not sure what your TE are though. You should get a change in height of about 0.487m.

Regards,
-Hoot

13. Apr 13, 2006

### skittlesj526

yeah, i got 48.73 cm which converts about the same but now i have:
mgh+1/2 mv2=1/2 mv2

how will the masses cancel?

14. Apr 13, 2006

### Hootenanny

Staff Emeritus
$$mgh + \frac{1}{2}mv_{i}^{2} = \frac{1}{2}mv_{f}^{2}$$

Simply divide throughout by $m$

Regards,
-Hoot

15. Apr 13, 2006

### skittlesj526

i got an ending velocity of 15.42 m/s

16. Apr 13, 2006

### Hootenanny

Staff Emeritus
I don't think thats correct. Can you show your working?

Regards,
-Hoot

17. Apr 13, 2006

### skittlesj526

just seemd kinda large, doesn't it?

18. Apr 13, 2006

### skittlesj526

that would be cm/s

19. Apr 13, 2006

### Hootenanny

Staff Emeritus