Conservation of Energy Problems [help]

[krypt0nite]

1) Tarzan is running at top speed (6.0m/s) and grabs a vine hanging vertically from a tall tree.
a) How high can we swing upward?
b) Does the length of the vine affect the answer?

Ok, where do I start. Don't you need the mass to solve this kind of problem??

2) In the high jump, the KE of an athlete is transformed into gravitational potential energy without the aid of a pole. With what minimum speed must the athlete leave the ground inorder to lift his center of mass 2.10m and cross the bar with a speed of 0.80 m/s?

Don't understand. period.

 

[AKG]

1) Tarzan is running at top speed (6.0m/s) and grabs a vine hanging vertically from a tall tree.
a) How high can we swing upward?
b) Does the length of the vine affect the answer?

Ok, where do I start. Don't you need the mass to solve this kind of problem??

The title of this thread is "Conservation of Energy Problems [help]". So, think about what kind of equation you can set up. If we take the ground as our reference, how much gravitational potential energy will Tarzan have? Given that he's running, how much kinetic energy? Now, when he reaches the top of his swing, how much kinetic energy will he have? To answer the previous question, answer this one first: what will his speed be at the top of his swing? Can you use the answers to all those questions to find the final gravitational energy at the top of the swing? Set up an equation and you'll see.

2) In the high jump, the KE of an athlete is transformed into gravitational potential energy without the aid of a pole. With what minimum speed must the athlete leave the ground inorder to lift his center of mass 2.10m and cross the bar with a speed of 0.80 m/s?

Don't understand. period.

Don't understand, period? These problems are very common, surely you have conservation of energy problems/examples in your textbook. As a general rule:

$$E_{total}\mbox{ remains constant}$$
$$E_{total}\ =\ K_{initial}\ +\ U_{initial}\ =\ K_{final}\ +\ U_{final}$$

...where "K" represents kinetic energy and "U" represents potential energy.

Also, you should be using the formulas:

$$K_{translational}\ =\ \frac{1}{2}mv^2$$
$$U_{gravitational}\ =\ mg\Delta h$$

 

[TALewis]

1st problem:

One of the fun things about doing physics problems is finding out the stuff that doesn't matter. "Missing" information is often a stumbling block for students who notice something such as "there's no mass given" and don't know where to start. The solution is to do the problem anyway as if you had been given the mass, but to just call it m instead of a number. If it is truly unnecessary, it will "fall out" of your equations.

Tarzan starts with zero potential energy and all kinetic energy. He ends up at the highest point of his swing with zero kinetic energy and all potential energy. We write most simply:

$$\frac{1}{2}mV^2 = mgh$$

Immediately it can be seen that m is on both sides of the equation and can be divided out. You can solve what's left for h.

For part b: If we accept that the equation above completely describes the simplified situation of the problem, then the fact that the length of the rope isn't mentioned anywhere in the equation should tell us that it doesn't matter how long the rope is. All that matters is Tarzan's initial speed, from which comes his initial kinetic energy, the starting energy of the system.

Also, the mere fact that you are given part 1a with the expectation that you can solve it answers part 1b for you: if you needed the length of the rope, you wouldn't have been able to solve part 1a without it.

 

[krypt0nite]

Yea, I understand now.
Well I found 2 ways to solve these problems. You can also use the equations of motion and the KE=PE equation to solve it as well.

Tarzan will move up 1.8m.
And the intial velocity of the number 2 is 6.5m/s.

 

[TALewis]

Yes, there are many ways to solve a given problem like this. In a traditional physics or mechanics course, you might see these problems first posed in the context of the equations of motion. Later in the text, you could see the identical problem in the chapter about conservation of energy. One of my professors likened it to a "toolbox." You've got a lot of tools you can use to solve any given problem. Often, a combination of motion equations, conservation of energy, and conservation of momentum is most effective. It's a matter of which method you're most comfortable with, and using the right tool for the job.

Edit: Oh, and your answers look right too.