There MUST be steps to solving problems dealing with Conservation of Energy No?

[riseofphoenix]

There MUST be steps to solving problems dealing with Conservation of Energy! No?

There just HAS to be... like Step 1) What does the problem give you...
Step 2) Was does the law of Conservation of Energy state

Etc Etc...
For example...16. A 66.0-kg person throws a 0.0480-kg snowball forward with a ground speed of 31.0 m/s. A second person, with a mass of 55.0 kg, catches the snowball. Both people are on skates. The first person is initially moving forward with a speed of 2.30 m/s, and the second person is initially at rest. What are the velocities of the two people after the snowball is exchanged? Disregard the friction between the skates and the ice.

Thrower: ______ m/s
Catcher: ______ m/s

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This practice test my teacher gave our class has a LOT of problems dealing with the ONE single, SEEMINGLY STRAIGHTFORWARD, concept of Conservation of Energy! There HAS to be a certain amount of steps I have to take in order to approach ANY problem dealing with Conservation of Energy, right?? Can anyone list steps I have to take in order to approach problems like these? Because my approach almost NEVER works!

This is what I did - the fact that I just CAN'T seem to fully UNDERSTAND these types of problems is SO frustrating that I'm literally fuming and I can't think straight. And I'm such a lOGICAL thinker, which explains why I NEED to know that there is some kind of pattern in these problems!

To find speed for thrower:

1) Energy system of thrower vs. Energy system of catcher (?)

PE_A + KE_A = PE_B + KE_B
0 + (1/2)mv² = 0 + (1/2)mv²
(1/2)(66)v² = (1/2)(55)(2.30 - 0)²
v² = 145.475/33
v = √(4.4083)
v = 2.09 m/s

"INCORRECT" Correct answer is - Thrower: 2.28 m/s

??
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F. My. Life.

-.-

Help anyone?

 

[riseofphoenix]

So my question is... can someone PLEASE help me come up with a Series of STEPS to follow for ANY kind of physics problem dealing with the Conservation of Energy?
Starting with this problem (of course)

 

[riseofphoenix]

Step 1) Work being done on object by external forces or by internal forces?

No external forces are doing work on the two skaters. However, internal forces are doing work on the two skaters. Therefore, mechanical energy (KE + PE) is conserved. Meaning,

KE_initial + PE_initial = KE_final + PE_final (the same)


Step 2) Identify your two energy systems

Energy system A (E_A) - Thrower: KE_A + PE_A
Energy system B (E_B) - Catcher: KE_B + PE_B

Step 3) ?

 

[HallsofIvy]

Why are you so concerned with "steps"? Just write out the equations the conservation laws give you and solve the equations! However, you will need to think about two things: the conservation of mechanical energy does not apply to the first person because he uses muscle energy to throw the ball and conservation of energy alone is not sufficient- you have to use "conservation of momentum" also.

 

[riseofphoenix]

Why are you so concerned with "steps"? Just write out the equations the conservation laws give you and solve the equations! However, you will need to think about two things: the conservation of mechanical energy does not apply to the first person because he uses muscle energy to throw the ball and conservation of energy alone is not sufficient- you have to use "conservation of momentum" also.

Because I need to piece this together and understand it...
There are going to be 2 conceptual questions on the test!

Also... what is conservation of momentum?

Is it p = mv?

 

[riseofphoenix]

Are you still there?

 

[aralbrec]

For energy conservation, you have to identify a system by drawing a box around something and saying any energy in this box is conserved (energy could cross the box's boundary too, in which case you would have to consider that!). You can say mechanical energy is conserved if there are no unidentified forces outside the box acting on things inside the box. Things like gravity of the Earth, which is an outside force, are taken into account with potential energy and this must also be done with any other outside agents affecting the system.

You seem to be taking your system to include the two people and the snowball.

Then, as you have found, your conservation equation becomes:

energy before = energy after
0.5*(m1+msnowball)*v1^2 = 0.5*m1*v1f^2 + 0.5*(m2+msnowball)*v2f^2

m1,v1 refers to person one initially moving and m2,v2 refers to person two initially at rest. The snowball is attached to the relevant person. Note the mass of the snowball is relatively small so won't affect the computed values much.

This is one equation and two unknowns. You don't have enough information to solve it. The suggestion of using conservation of momentum to find another may generate another equation but it is also predicated on some assumptions about the snowball impact and throw (Do you know about momentum conservation yet?)However there is another way. The clue is you realize the snowball is going to be transferring energy from one person to the other, so use it as a medium to exchange energy between two systems.

Let's choose another system that only includes the person throwing the snowball and the snowball itself.

energy before = energy after
0.5(m1 + msnowball)*v1^2 = 0.5*m1*vf^2 + 0.5*msnowball*vsnowball^2

This is before the snowball is tossed to after the snowball leaves the person's hand. Since the person is carrying the snowball initially, the snowball must be moving at the same speed initially.See if you can come up with another equation for person2 and the snowball. Begin with the snowball moving and ending with the snowball attached to person2.Now I quickly did this and came up with a different answer than the 'correct answer'. Let's see if it was sloppy quick calculation or something else from other responses.

 

[Doc Al]

This is a conservation of momentum problem. (Mechanical energy is not conserved here.)

 

[riseofphoenix]

Yeah but...

What's the difference between Conservation of Energy and Conservation of Momentum?

Conservation of Energy: PE(initial) + KE(initial) = PE(final) + KE(final)
Conservation of Momentum: m1v1 = m2v2?

You know something is Conservation of Energy when you have: work being done on an object by INTERNAL forces

You know something is Conservation of MOMENTUM when you have: mass and velocity, and a moving body/object

Like, how would I know that this problem deals with Conservation of Momentum (and not Conservation of Energy)?

And to solve the problem, would I do:

(mv)_initial = (mv)_final?

What next? Because they want the velocites of the TWO people after the snowball is exchanged...

 

[riseofphoenix]

So Essentially...

Conservation of Energy: involves an object that has PE at one point and KE at one point; work being done on an object by INTERNAL forces

Equation to use: PE_(initial) + KE_(initial) = PE_(final) + KE_(final) ​

Conservation of Momentum: when you have mass and velocity, and a moving body

Equation to use: p_initial = p_final​

Equation to use: mv_initial = mv_final​

Equation to use (more than 1 mass): m₁v_initial + m₂v_initial = m₁v_final+ m₂v_final​

 

[Doc Al]

Some additional tips for analyzing this sort of problem:

When you throw something: Is mechanical energy conserved? No, not usually. Think about it: You are sitting still (say) on a sheet of ice. So your initial KE = 0. You throw a rock, so both you and the rock are now moving and have KE. Thus the final KE > 0.

Is momentum conserved? Yes! No external forces are involved.

When you catch something: Is mechanical energy conserved? No, not usually. When you catch something, that's an example of a perfectly inelastic collision. KE is not conserved.

Is momentum conserved? Yes! No external forces are involved.