FIG. 4.18 The law of universal gravitation is an inverse square law
STS
Every mass has gravity. Even you! However it takes a large mass to exert a tangible force. We generally only notice gravity from planets or stars. Our solar system is interlocked in a set pattern due to the combined gravitational forces of each planet and object, as well as of our Sun. If you removed one object, the order of the solar system could dramatically change.
Earth F1 F2 weightlessness FIG. 4.19 The point of weightlessness
• G is the universal gravitational constant (G = 6.7 × 10−11 N m2 kg−2). It was discovered by Henry Cavendish in 1731.
• •
Gravity holds the atmosphere in place. Smaller masses such as the Moon have a weaker gravitational force and cannot sustain an atmosphere.
Even mountains can exert a small horizontal gravity due to their mass but it takes sensitive measuring equipment to demonstrate this.
QUESTIONS AND ANSWERS g = 9.8 m s−2
5. A girl of mass 40 kg is holding a bag weighing 10 N. What is the upward force exerted by the floor on her?
Solution
Combined weight of girl and bag = (40)(9.8) + 10 = 402 N
The force exerted by the floor is equal and opposite, so is 402 N.
6. Calculate the gravitational attraction of two spheres of mass 10 kg each, with a distance of 30 cm between their centres.
Solution F =
_________ d2 = (6.7 × 10−11)(10)(10)
Gm1m2 = 7.44 × 10−8 N Continued 38 FUSION
__________________________ (0.3)2
point of Moon 3d 3M d 2M b 2M d M attractive force 2F d 2M attractive force 4F
Because the law of universal gravitation is an inverse square law (Fig. 4.18):
• if you double the distance, you quarter the force • if you halve the distance, you multiply the force by 4 • if you treble the distance, you have one-ninth the force.
Notes about gravitational force •
Gravitational force is always attractive. •
Bodies may be considered as point masses and the distance between them is taken as the distance between their centres.
• The size of the gravitational force is equal for both masses. •
The point between two masses at which a body is weightless is where the masses’ attractive forces cancel (Fig. 4.19).
