Getting Off the Earth

Focus 2 Part 2

Keeping us on the EarthNewton said (in 1687) that all objects exert a

force on all other objects in the universe. This force is gravity

define Newton’s Law of Universal Gravitation

F = Gm1m2/d2

present information and use available evidence to discuss the factors affecting the strength of the gravitational force

solve problems and analyse information using

F = Gm1m2/d2

221

d

mmGFg

Where:

Fg = force of gravity between two masses (N)

G = universal gravitation constant = 6.67 x 10-11 N m2 kg-2

m1 and m2 = the two masses involved (kg)

d = the distances between their centres of mass (m)

IMPORTANT – G is not the same as g!

Mass 1m1

Mass 2m2

d

Fg

The force is exerted equally on each mass (Newton’s Third Law)

Example CalculationCalculate the force of gravity between the Earth and a 65 kg Physics student.

Data: Mass of the Earth = 5.97 x 1024 kgMass of the student = 65 kgRadius of the Earth = 6.38 x 106 m

Equation: 221

d

mmGF

26

2411

)1038.6(

651097.51067.6

F

).2(640 figssigNF

Q. Does this answer make sense?

Q. Why is the answer only to 2 significant figures?

Have a Go!Calculate the gravitational force of

attraction between you and the person sitting next to you.

Assume that you both have a mass of 65 kg and that you are sitting 1.0 m apart.

Compare your answer to the weight force between you and the Earth(640 N as calculated previously)

Newton’s Ideas about Escape Velocity Newton imagined what would happen to the range of a

projectile if you shot it faster and faster from a canon.Since the faster the initial velocity, the longer the range,

he decided it should be possible to launch a projectile fast enough so that it achieves an orbit around the earth.

Newton hypothesized that if the canon ball is shot fast enough, as the ball falls, the Earth will curve away at the same rate, so the ball won’t fall to the Earth - it will be in orbit. The velocity needed to achieve this is called the escape velocity.