Work done (1 Viewer)

[Hypem]

In a trial HSC exam:

Q22) A satellite is planned to be placed in a circular orbit 20 500km above the Earth's surface to be part of a GPS array. The satellite has a mass of 1000 kg.

(radius of earth = 6380 km, mass not sure, maybe 6 x 10^24)

(a) Calculate the GPE of the satellite before it is launched.

- This is all well and good, it is -6.27 x 10^10 J.

(b) Calculate the amount of work done against gravity to raise the satellite to its final orbit.

- This is where I get confused. I thought work done was equal to Ep(final) - Ep(initial), and it's always a positive answer when moving something from a lower point to a higher point?

Well, they've done it like this:

GPE at 22,500 km above earth is -1.4888 x 10^10.... (all well and good so far)

Ep(initial) - Ep(final) = Work done

-6.27272727 x 10^10 - ( -1.488839286 x 10^10)

= -4.782 x 10^10 J

 

[Parvee]

Since GPE= -GmM/r
Then Work Done= GPE(final)-GPE(initial)= -GmM/rf - (-GmM/ri)
Therefore Work Done = -GmM/rf + GmM/ri = GPE(initial)-GPE(final)

 

[Hypem]

But using either of those will give either a + or - result. Which one is correct?

 

[Nws m8]

In a trial HSC exam:

Q22) A satellite is planned to be placed in a circular orbit 20 500km above the Earth's surface to be part of a GPS array. The satellite has a mass of 1000 kg.

(radius of earth = 6380 km, mass not sure, maybe 6 x 10^24)

(a) Calculate the GPE of the satellite before it is launched.

- This is all well and good, it is -6.27 x 10^10 J.

(b) Calculate the amount of work done against gravity to raise the satellite to its final orbit.

- This is where I get confused. I thought work done was equal to Ep(final) - Ep(initial), and it's always a positive answer when moving something from a lower point to a higher point?

Well, they've done it like this:

GPE at 22,500 km above earth is -1.4888 x 10^10.... (all well and good so far)

Ep(initial) - Ep(final) = Work done

-6.27272727 x 10^10 - ( -1.488839286 x 10^10)

= -4.782 x 10^10 J

The work done is negative because the 0 of the potential energy is defined at infinity....so even if you move something from lower to higher point, it will still be negative .... because the distance moved does not reach infinity ....

 

[Nws m8]

But using either of those will give either a + or - result. Which one is correct?

negative is correct, WORK DONE is ALWAYS NEGATIVE because the zero of potential energy is defined at infinity anything below that infinite distance is negative

 

[someth1ng]

The work done is negative because the 0 of the potential energy is defined at infinity....so even if you move something from lower to higher point, it will still be negative .... because the distance moved does not reach infinity ....

Why would that mean that it has to be negative?

Positive work is done if you lift an object upwards since you apply a force upwards and the object also moves upwards.

 

[Nws m8]

Why would that mean that it has to be negative?

Positive work is done if you lift an object upwards since you apply a force upwards and the object also moves upwards.

You are right but in this case, we don't use PE = mgh as satellite is near the 'surface', and near surfaces or in outer space, we use the other equation ..... and
Because the zero of PE is defined at infinity, and the distance moved doesn't equal infinity, therefore it is still below ZERO i.e. negative

 

[someth1ng]

- This is where I get confused. I thought work done was equal to Ep(final) - Ep(initial), and it's always a positive answer when moving something from a lower point to a higher point?

Ep(initial) - Ep(final) = Work done

1. First one is correct.
2. Remember that Change of GPE=Work Done --> Change=final-initial.

Because the zero of PE is defined at infinity, and the distance moved doesn't equal infinity, therefore it is still below ZERO i.e. negative

But the change can still be positive.

 

[someth1ng]

You are right but in this case, we don't use PE = mgh as satellite is near the 'surface', and near surfaces or in outer space, we use the other equation ..... and
Because the zero of PE is defined at infinity, and the distance moved doesn't equal infinity, therefore it is still below ZERO i.e. negative

It doesn't matter.

We use Ep=-m1m2/d^2 and the change is Ep(final)-Ep(initial) which is ALWAYS positive if the object is ascending.

 

[someth1ng]

IT DOES MATTER , you have to put negative to state work done is negative and so the examiner know you know the concept

Yeah, the point is that in this case, it is positive work, not negative work.

GPE=mgh is used close to the surface where g is basically constant, in locations where g varies (long distances), GPE=-Gm1m2/d^2. If in doubt, use GPE=-Gm1m2/d^2.

Now, look. To lift the object, you need to apply some sort of upward force - if the object moves upwards, you are doing positive work.

 

[Hypem]

So confused...is the negative sign simply because "descending down/toward Earth = -" and "ascending away from Earth = +". So that would make the work done positive since it's ascending, as someth1ing said?

btw GPE doesn't have distance as a square.

 

[Nws m8]

So confused...is the negative sign simply because "descending down/toward Earth = -" and "ascending away from Earth = +". So that would make the work done positive since it's ascending, as someth1ing said?

btw GPE doesn't have distance as a square.

It's -ve, even the answer has a -ve

 

[iBibah]

negative is correct, WORK DONE is ALWAYS NEGATIVE because the zero of potential energy is defined at infinity anything below that infinite distance is negative

This is incorrect:

Despite gravitational potential energy being negative, the change in gravitational potential energy can be positive. Work done is defined as the change in gravitational potential energy. So if an object is moved against a gravitational field, then positive work is done, hence the change in gravitational potential energy is positive. Work done is given by the following equation:

Hence if the initial radius from the centre of the gravitational field is less than that of the final, then change in GPE (aka Work Done) will be positive.

 

[iBibah]

So confused...is the negative sign simply because "descending down/toward Earth = -" and "ascending away from Earth = +". So that would make the work done positive since it's ascending, as someth1ing said?

btw GPE doesn't have distance as a square.

So this is correct

 

[Parvee]

But using either of those will give either a + or - result. Which one is correct?

The answer should be positive.
I'll try explain this in terms of numbers :L
GPE is the most negative at the surface of the earth hence when the satellite is placed in orbit it has a 'larger' i.e. less negative GPE
Since Work Done= GPE(initial)-GPE(final)
This would be a small negative number + a larger postive number hence giving a positive answer

Not sure if this makes too much sense lol
Its easier to explain in person

 

[treebrains]

slightly off topic... is it valid to also calculate work done using change in KE, given you know the linear orbital velocity?