HSC Space: Section 1

Weight

• Whenever a mass is located within a gravitational field it experiences a force. It is that force, due to gravity, that you call weight.

• Weight is that force that acts on a body within a gravitational field and is equal to the mass of the body multiplied by the rate of acceleration, called g.

• Using Newton's Second Law we are able to define a formula for weight:

Question

1. What is the weight of a person with a mass of 65.0 kg?

2. The same person climbs Mt Everest. Acceleration due to gravity at the peak, at 8.8 km above sea level, is 9.77 ms-2. Calculate the person’s weight now.

ANS: 637N and 635N

The value of ‘g’

• It is important that you realise that the force described as weight also fits the equation shown below (Newton's Law of Universal Gravitation), because it is the force between two masses, one of which is the Earth.

Activity

Using the previous equations find the weight of your phone will be on each planet.Mass of phone: __________

Variations in ‘g ’

• The acceleration due to gravity, can be different to the normally accepted value of 9.80 ms-2. There are a number of factors that can cause this value to vary around the world. These factors are listed below.– The Earth’s crust varies in thickness and density because of such

things as tectonic plate boundaries and different density mineral deposits.

– The Earth is flatter at the poles. This means that the poles are closer to the centre of the Earth, so that the value of g will be greater at the poles.

– The centrifuge effect created by the spin of the Earth, reduces the value of g. This effect is greatest at the Equator and least at the poles.

Practical: Determing ‘g’

• To figure out 'g' using your T2 vs l graph you need to first obtain the gradient from your graph. This can be done by plotting a trendline on your graph and displaying the equation. Use this to work out the gradient using the maths equation y = mx + b.

• Once you have your gradient you need to compare the period equation with the maths equation y = mx + b.

Gravity

• Video

Gravity

• Consider this question:

• How far does someone have to be to be able to escape the effect of the Earth's gravity?

Gravity (cont)

• 'g' depends on the inverse of the square of the distance from the centre of the Earth. It means that as distance increases, the value of 'g' reduces quickly.

• However it never actually drops to zero until the distance equals infinity.

• In other words, the influence of the Earth’s (and any other celestial body) gravity extends very far out into space but drops off in strength very quickly with that increasing distance. A good way to describe this infuence is to say that it is a ‘gravitational field’.

Gravity (cont)

• There are gravitational fields around celestial objects within which gravitational forces will act on a mass. In fact, there are gravitational fields around any mass but the mass must be huge for the forces to become noticeable.

Gravitation Potential Energy Ep

• Consider the energy of a mass within a gravitational field.

• You have already seen that a mass within a gravitational field will experience a force (its weight).

• If that force meets no resistance, like a floor, then the mass will fall and as it falls it speeds up and gains kinetic energy.

• But energy cannot be created, so where does that kinetic energy come from?

• The answer is that the mass has energy to begin with.

• This energy is called ‘gravitational potential energy’; it has the symbol Ep and the units joules (J).

• As the mass falls it has less and less gravitational potential energy (because its being converted into more and more kinetic energy).

• Therefore it is moving away from positions of higher potential energy and towards positions of lower potential energy.

Gravitation Potential Energy Ep

• The next thing to consider is the location of the zero potential energy level. In other words, at what position would a mass have to be in order to have no gravitational potential energy at all?

Gravitation Potential Energy Ep

• In order to be completely free of a gravitational field a mass must lie an infinite distance away. Infinity, then, is our zero level: Ep = 0 at ∞.

• If you were to place a mass, say, ten kilometres above the surface of the Earth and let it go it would fall toward the Earth. It is falling away from the zero level (which is at infinity), and yet it is falling to points of lower and lower gravitational potential energy.

Gravitation Potential Energy Ep

• This means that its gravitational potential energy is negative, and its most negative value will be at the surface of the Earth! This idea can be a little hard to grasp at first.

Gravitation Potential Energy Ep

• The gravitational potential energy Ep of a mass at one point is equal to the change in gravitational potential energy that occurs when moving the mass from the zero level (infinity) to the point.

• This is defined as the work done to move the object from infinity (or from a very large distance away) to the point.

• When work is done, energy has been converted from one form to another. It can be shown mathematically that the gravitational potential energy is given by the following equation:

Defining Gravitation Potential Energy Ep

Gravitation Potential Energy Ep on Earth

• On (or near) Earth (where g is constant - remember the uniform gravitational field with parallel lines), zero can be taken to be on the surface, and objects lifted to height h have a positive Ep=mgh

• Remember: work done = energy used

• YOU CANNOT USE THIS FOR ASTRONOMICAL CALCULATIONS! Remember the value of ‘g’ changes as you get away from the surface of the Earth.

Gravitation Potential Energy Ep

• Video

End of Section 1