Physics HSC Space
Notes and Questions by Dot Point
1. The Earth has a gravitational field that exerts a force on objects both on it and around it
. define weight as the force on an object due to a gravitational field
o perform an investigation and gather information to determine a value for acceleration due to gravity using pendulum motion or computer-assisted technology and identify reason for possible variations from the value 9.8 ms-2 o gather secondary information to predict the value of acceleration due to gravity on other planets o analyse information using the expression:
F mg to determine the weight force for a body on Earth and for the same body on other planets
Recall that Newton’s Law of Universal Gravitation describes the force of attraction between two masses m1 and m2 separated by a distance r as
2 F = Gm1m2 / r where G is the universal gravitational constant and is equal to 6.67 x 10-11 Note that some references use d for distance of separation.
The weight force of an object (say mass m2) is equivalent to the force which the Earth exerts on that object as a result of it being in the Earth’s gravitational field, and that the expression for the weight force of an object of mass m2 is
W = m2g where g is the acceleration due to gravity We can therefore equate these two expressions as they both describe the same force. We derive the formula
2 g = Gm1 / r which can be applied to any mass m1 which is generating a gravitational field. This formula can be used to determine the acceleration due to gravity at any distance above the Earth’s surface. We must remember that the value of r will be given by the radius of the Earth plus the distance above the Earth’s surface. 1. (a) Determine the acceleration due to gravity at an altitude of (i) 100 km above the Earth’s surface (ii) 200 km above the Earth’s surface ………………………………………… ………………………………………………… ………………………………………… ………………………………………………… ………………………………………… ………………………………………………… ………………………………………… ………………………………………………… Physics HSC : Space Syllabus Section 1 : Notes by Dot Point : page 1 (b) Explain the fact that although the distance has been doubled, the value of g in part (ii) is NOT one quarter of the value of g in part (i). ………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… …………………………………………………………………………………………………
The formula can also be used to calculate the acceleration due to gravity on any other massive body, so long as the mass and the radius of the body are known.
2. Determine the value of g on Mars, given that its mass is 6.6 x 1023 kg and its radius is 3.4 x 106 m. …………………………………………………………………………………………………………… ……………………………………………………………………………………………………………
A variation on this question is to provide the student with the mass of the body in terms of the mass of the Earth i.e. Mercury: 0.06 Earth masses; and the radius of the body in terms of the radius of the Earth i.e. Mercury: 0.38 Earth radii. Knowing the value of g on Earth is 9.8, we can use the above values to calculate the value of g on Mercury.
3. The following data applies to Pluto: radius compared to Earth 0.18; mass compared to Earth 0.002. Verify that the gravitational acceleration on Pluto is 0.6 ms-2. …………………………………………………………………………………………………………… ……………………………………………………………………………………………………………
Also note that a relationship exists between the value of g and the distance from the centre of mass of the object. The distance squared occurs in the denominator of the formula, so you should be able to see that the relationship will be an inverse square relationship. Thus if the distance of separation is doubled, the value of g will become a quarter of its previous value.
4. Sketch a graph of gravitational field strength vs. distance.
Physics HSC : Space Syllabus Section 1 : Notes by Dot Point : page 2 Students should also be aware that in moving from one planetary body to another, the mass of an object will remain the same, but the weight of the body may vary. Thus a mass of 10 kg on Earth has a weight of 98 N. However the same 10 kg mass on the moon, where the acceleration due to gravity is 1.62 ms-2, will have a weight of 16.2 N.
5. The weight of a body on the moon is 8.10 N. Determine (a) the mass of the body, and (b) the weight of the body on Earth …………………………………………………………………………………………………………… ……………………………………………………………………………………………………………
6. A student employed the following method for determining a value of g. Recognising that s = ut + 1/2at2 and that for an object dropped from rest u = 0 s = 1/2at2 the student reasoned that if an object were dropped through a distance of, say 4.9 m, and timed over this journey, then a value of a (hence g) could be determined. The student’s reasoning is valid, but he obtained poor results for g. Comment on any deficiencies you can see in this method. …………………………………………………………………………… …………………………………………………………………………………………………………… …………………………………………………………………………………………………………… …………………………………………………………………………………………………………… 7. The accepted value of the acceleration due to gravity is 9.8 ms-2. Discuss one method of determining a value for g which could be employed in the school laboratory. …………………………………………………………………………………………………………… …………………………………………………………………………………………………………… …………………………………………………………………………………………………………… ……………………………………………………………………………………………………………
Please attempt the assignment containing questions from past examination papers. The assignment is called Space Syllabus Section 1 Assignment A. The assignment can be downloaded from the school’s Moodle site.
Physics HSC : Space Syllabus Section 1 : Notes by Dot Point : page 3 . explain that a change in gravitational potential energy is related to work done . define gravitational potential energy as the work done to move an object from a very large distance away to a point in a gravitational field m m E G 1 2 p r
You may recall that the gravitational potential energy (GPE) of a body increases as the distance above the Earth’s surface increases. In simple terms this is because the potential of the body to perform work increases as the height increases. Thus the GPE is dependent on two variables i.e. its mass and its height above the Earth’s surface. The formula is GPE = mgh where m is the mass of the body and h is its height above the Earth’s surface The formula is valid because to lift the body to a greater height requires that we must do work on the body i.e. we must exert a force to change the displacement of the body. In this case the force is the weight force of the body and its change in displacement is given by the change in height. Thus, from the formula W = Fs, we have W = GPE = mgh where W is the work done and GPE represents the change in GPE This equation is appropriate when discussing objects near the Earth’s surface. For objects much further from the Earth’s surface e.g. satellites, an apparently different definition and therefore a different formula, is used. The only real difference, however, is that we define zero potential as being at an infinite distance from the Earth. As a consequence of this, and the fact that gravitational potential increases as you move away from the Earth, all other gravitational potentials are negative! The formula is GPE = -GMm / r where G is the universal gravitational constant M is the mass of the planetary body m is the mass of the body in the gravitational field r is the distance of separation of the centres of the two masses. Notice that in this situation we are only really interested in the change of GPE as it is lifted to a certain height above the Earth’s surface, so the minus sign in the formula is not always necessary.
1. A satellite of mass 200 kg is in orbit 250 km above the Earth’ surface. Determine its gravitational potential energy. …………………………………………………………………………………… …………………………………………………………………………………………………………… 2. If the satellite in Qu. 1 is now boosted into an orbit whose radius is 42 000 km, determine the change in GPE. …………………………………………………………………………………………………… ……………………………………………………………………………………………………………
Physics HSC : Space Syllabus Section 1 : Notes by Dot Point : page 4 3. We have learnt previously that for objects close to the Earth’s surface the work done on the object is equal to the increase in its GPE. Is this the case in Qu. 2? Discuss. …………………………… …………………………………………………………………………………………………………… …………………………………………………………………………………………………………… …………………………………………………………………………………………………………… 4. The Hubble telescope has a mass or 11.350 tonnes and is orbiting at an altitude of 320 km. Determine the GPE possessed by the Hubble telescope. …………………………………………………………… …………………………………………………………………………………………………………… ……………………………………………………………………………………………………………
Please attempt the assignment containing questions on this dot point from past examination papers. The assignment is called Space Syllabus Section 1 Assignment B. The assignment can be downloaded from the school’s Moodle site.
Physics HSC : Space Syllabus Section 1 : Notes by Dot Point : page 5