A few questions in relation to energy

In summary: ATH 301 assignment 3:In summary, we discussed elastic collisions between objects of different masses, where momentum and kinetic energy are conserved. It is possible for the objects to move off at right angles to each other after the collision. We also explored the relationship between impulse and work, where an object can receive an impulse without work being done on it and vice versa. Finally, we looked at a satellite in circular orbit losing energy through friction and increasing speed due to its change in potential energy.
  • #1
lektor
56
0
we were assigned a few to find answers to, the following ones stumped me, hopefully you can help :)

When two objects of different masses collide and the collision is elastic, it is said that the two objects will always move off at right angles to each other.
Is this likely to be true? Explain

Can an object, perhaps in motion, receive an impulse without having work done on it?
Conversely, can an object have work done on it without receiving an impulse?


3) If a satellite in circular orbit around the Earth encounters the outer fringes of the atomosphere, it begins to lose energy through friction. Yet the result is that it increases speed, Why is this?

idea for 3) Is this because it Moves closer to the Earth and has a greater force of gravity acting upon it
 
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  • #2
1) It is not necessary that the balls always travel prependicularly to each other after collision.In elastic collision both momentum and kinetic energy is conserved and there is no energy loss through heat or sound.Both the cases are possible.


2)Impulse is basically Force/second. So if the force is applied for a short time in a such a way that no displacement occurs,no work is done by the impulse.Example, drop a ball over a block kept on a smooth surface.


3) Orbital velocity of a satellite in arbit of radius "r" from the centre of the Earth is given by:

[itex]
\sqrt{\frac{GM}{r}}
[/itex]

As r decreases, its orbital velocity decreases and it loses energy.By losing energy, it does not mean it loses its kinetic energy.Net energy of a satellite in its orbit is given by:

[itex]
\frac{-GMm}{r}
[/itex]

Therefore as r decreases ,its energy decreases due to the minus sign.As the above energy is the sum of [Kinetic Energy+ Potential Energy] Therefore ,as its orbital velocity increases when it loses some potential Energy.

Therefore,
THE SATELLITE GAINS KINETIC ENERGY ON ACCOUNT OF LOSING POTENTIAL ENERGY WHEN IT COMES NEAR TO EARTH.
 
  • #3
lektor said:
we were assigned a few to find answers to, the following ones stumped me, hopefully you can help :)

When two objects of different masses collide and the collision is elastic, it is said that the two objects will always move off at right angles to each other.
Is this likely to be true? Explain
Yes. If you play pool, it is very useful because it allows you to play 'shape'. Otherwise you will not be able to predict where the cue ball goes.

Since [itex]\vec v_1 + \vec v_2 = \vec v_0[/itex] (momentum conserved) and [itex]v_0^2 = v_1^2 + v_2^2[/itex] (energy conserved) the vector diagram of the collision defines a triangle in which v0 is the hypotenuse whose length is related to the sides by the pythagorean formula. This means the angle between v1 and v2 is a right angle).

Can an object, perhaps in motion, receive an impulse without having work done on it?
Conversely, can an object have work done on it without receiving an impulse?
If [itex]F_{net}dt = (dp/dt)dt \ne 0[/itex] then dp is nonzero. [edit:] This means that its velocity must change. But, of course, this does not necessarily its speed changes - the change could be in direction only (speed is unchanged). If the direction of the force and momentum are perpendicular to each other, there is a change of momentum but no change in speed - hence no change in energy.

3) If a satellite in circular orbit around the Earth encounters the outer fringes of the atomosphere, it begins to lose energy through friction. Yet the result is that it increases speed, Why is this?

idea for 3) Is this because it Moves closer to the Earth and has a greater force of gravity acting upon it
It increases vertical speed as it loses its tangential speed. This is because as it slows its orbital speed it falls toward the Earth and thus loses gravitational potential energy. This loss of potential results in an increase in kinetic energy (ie energy is conserved).

AM
 
Last edited:

Related to A few questions in relation to energy

What is energy and why is it important?

Energy is the ability to do work or cause change. It is essential for all living organisms and is needed for everyday tasks such as cooking, transportation, and powering electronic devices. Without energy, life as we know it would not exist.

What are the different forms of energy?

Energy can exist in various forms, including mechanical, thermal, electrical, chemical, nuclear, and electromagnetic. Each form of energy has its own unique properties and can be converted into another form.

How is energy produced and consumed?

Energy can be produced through various methods, including burning fossil fuels, nuclear reactions, and renewable sources such as solar, wind, and hydropower. Energy is consumed when it is used to power machines, devices, and processes that require work to be done.

What is the difference between renewable and non-renewable energy?

Renewable energy comes from sources that can be replenished naturally, such as solar, wind, and hydropower. Non-renewable energy, on the other hand, is derived from sources that cannot be replenished, such as fossil fuels and nuclear energy.

What are the environmental impacts of using different forms of energy?

The production and consumption of energy can have various environmental impacts. Fossil fuels, for example, contribute to air pollution, climate change, and water pollution. Renewable energy sources, on the other hand, have minimal environmental impacts and do not produce greenhouse gas emissions.

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