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Set 7 Problem number 3
The strength of a gravitational field is defined to be the acceleration imparted to an
object with mass in that field. The weight of an object is the force exerted by the
gravitational field on it.
At the surface of the Earth, the strength of the gravitational field is
approximately 9.8 m/s ^ 2.
Assume that you have a mass of 72 kilograms.
- What is your weight on the surface of the Earth?
- On the surface of the Moon, the strength of the gravitational field is
approximately 1.5 m/s ^ 2.
- How much would you weigh there?
- On another planet, suppose that you weigh 2000 Newtons.
- What is the strength of the gravitational field there?
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)( 72 kg) = 705.6 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)( 72 kg) = 108 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 72 kilogram mass.
- This acceleration is 2000 Newtons/ 72 kilograms = 27.77778 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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