Help me figure out these true/false statements.

[xelda]

1) A ball is thrown from a tall building at some angle with respect to the horizontal. By measuring the height of the building and the distance that the ball lands from the base of the buiding, one can uniquely determine the speed of the ball when it hits the ground.
I put this down as false because wouldn't you need to know the angle?

2) The gravitational force between the Earth and the Moon results in work being done on the Moon.
False.

3) If only conservative forces act on an object, a decrease in the object's potential energy will always correspond to a decrease in its kinetic energy.
I'm confused at what this is asking, but I put this down as false.

4) Gravity is a conservative force. True.

5) If a rock, initially at rest, is dropped from a tall building, the speed of the rock when it hits the ground will only depend on its initial height above the ground. True

6) The total mechanical energy of a box sliding across a rough surface is conserved. True.

 

[Andrew Mason]

1) A ball is thrown from a tall building at some angle with respect to the horizontal. By measuring the height of the building and the distance that the ball lands from the base of the buiding, one can uniquely determine the speed of the ball when it hits the ground.
I put this down as false because wouldn't you need to know the angle?

Your answer is right but you don't need to know the angle. You would have to know its initial speed though (since it is thrown, not dropped). Its final kinetic energy is KE₀ + mgh. And from that you can find its speed.

2) The gravitational force between the Earth and the Moon results in work being done on the Moon.
False.

Incorrect. The moon is doing work at certain times during its orbit and at other times work is being done on it. The total net work done is close to 0 over one complete orbit. This is because the moon's orbit is not perfectly circular. The definition of power or work/unit time is $dW/dt = \vec F \cdot \vec v$. Because $\vec v$ is not always perpendicular to $\vec F$, there is some work being done.

3) If only conservative forces act on an object, a decrease in the object's potential energy will always correspond to a decrease in its kinetic energy.
I'm confused at what this is asking, but I put this down as false.

Correct. A conservative force is one where potential + kinetic energy is constant. If the force does work, the potential energy increases by that same amount (the moon in orbit is a good example). So a decrease in potential energy will always correspond to an increase in kinetic energy.

4) Gravity is a conservative force. True

Correct.

5) If a rock, initially at rest, is dropped from a tall building, the speed of the rock when it hits the ground will only depend on its initial height above the ground.True

Correct.

6) The total mechanical energy of a box sliding across a rough surface is conserved. True.

Incorrect. The box loses energy to heat. Friction is not a conservative force. It dissipates the energy.

AM

 

[xelda]

Thanks for your help! I can understand your explanations, but could you elaborate more on number 6? From what I've interpreted in the textbook, the total energy would be conserved due to the law of conservation of energy, isn't it?

 

[Andrew Mason]

Thanks for your help! I can understand your explanations, but could you elaborate more on number 6? From what I've interpreted in the textbook, the total energy would be conserved due to the law of conservation of energy, isn't it?

A conservative force is one for which the work done by it is fully recoverable (eg. converted to potential E). When work is converted to heat, the energy is dispersed and only a portion of the original work can be recovered from that heat (second law of thermodynamics).

AM

 

[BobG]

I wouldn't count on getting the right answer to number 2.

Andrew Mason's explanation is technically the correct explanation. But, is the question asking for that much detail or is it just poorly worded?

My first impression was that the answer is 'NO', since there can be no net work done. I would tend to look at the big picture and see the orbit can't change as a result of the Earth's gravity - the Moon would have to go through the exact same points over and over.

Even if the question intentionally left the word 'net' out, that's a lousy question - it would then be more of a pointless trick question - it would test your attention to detail instead of testing your knowledge of conservation of energy.

 

[HallsofIvy]

As far as #6 is concerned, it is important that it says mechanical energy.

In any "closed system", total energy is conserved (that's essentially why it's a "closed system") but heat is not "mechanical" energy.

 

[Andrew Mason]

I wouldn't count on getting the right answer to number 2.

Andrew Mason's explanation is technically the correct explanation. But, is the question asking for that much detail or is it just poorly worded?

My first impression was that the answer is 'NO', since there can be no net work done. I would tend to look at the big picture and see the orbit can't change as a result of the Earth's gravity - the Moon would have to go through the exact same points over and over.

Even if the question intentionally left the word 'net' out, that's a lousy question - it would then be more of a pointless trick question - it would test your attention to detail instead of testing your knowledge of conservation of energy.

That is always the problem with True/False questions! No room for explanation.

The question was: does the gravitational force between the Earth and the Moon result in work being done on the Moon? This was a college level question. If it had asked "does the gravitational force result in any net work being done on the moon in making exactly one complete orbit", the answer would be 'no'. But it doesn't ask that.

The moon's kinetic energy is being converted to potential energy all the time as the orbit is quite eccentric (as moons and planets go). So work is being done. Alot of work. The perigee-apogee at the present time is about 50,000 km or an eccentricity of about .065. It takes a lot of WORK to 'lift' a heavy object like the moon 50000 km - about $10^{28} J.$!

am