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Set 7 Problem number 3
The gravitational field strength at the surface of the Earth is g = 9.8
m/s^2; at the surface of the moon g is 1.5 m/s^2.
Suppose your mass is 66 kg.
- What is your weight on the surface of the Earth and on the Moon?
What is the strength of the gravitational field on the surface of a
planet where you weigh 2000 Newtons?
Your weight on Earth is equal to the force exerted on your mass by the
Earth's gravitational field.
- Since your mass would be accelerated at 9.8 m/s ^ 2 by this field, the
force must by Newton's Second Law be the product of your mass and this acceleration.
- Thus your weight is (9.8 m/s ^ 2)( 66 kg) = 646.8 Newtons.
- On the Moon, your weight would give your mass an acceleration of about
1.5 m/s ^ 2.
- Your weight there would thus be (1.5 m/s ^ 2)( 66 kg) = 99 Newtons.
- If your weight on a certain planet was 2000 Newtons, then the strength of
the gravitational field would be the acceleration that would result from application of
this net force to your 66 kilogram mass.
- This acceleration is 2000 Newtons/ 66 kilograms = 30.30303 meters/second ^ 2.
The strength of a gravitational field is defined as the acceleration experienced
by a mass on which the net force is that exerted by the field.
- The net force on a mass is equal to the product of the mass and its acceleration.
The force exerted on a mass m by a gravitational field with strength g must
therefore be F = m g.
- This force is the weight of the object: weight = m g.
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