Newton's Universal Law of Gravitation

BHS Physical Science K Warne

Mass & WeightMass (kg): This is a measure of

the amount of matter (number of kilograms) that makes up a body.

Weight (N):

• This is the force of gravity exerted on a body’s mass by the earth (planet).

Fg

1 kg

1 kg

1 kg

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Mass & Weight

Mass (m): Measured in kilograms

using a balance.

Force/Weight (Fg):

• Measured in Newton's using a spring balance or force meter.

1 kg

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9.8N

49 N

Falling Objects Two different object with different masses will

FALL at the same RATE.

• The force of gravity on 1kg of mass is 9.8 N.

• Each unit of mass has the same force on it!

• Each mass unit will have the SAME ACCELERATION.

1kg5 kg

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1kg

9.8 N

9.8 N

1kg

9.8 N

1kg

9.8 N

1kg

9.8 N

1kg

9.8 N

Motion of Falling objectTime (s) Displacem

ent (m)Average Velocity

Instantaneous Velocity

(m.s-1)

Acceleration (m.s-2)

0 0 0 0

5

20

45

4 80

5 125

6 180

1

2

3

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Gravitational Field Strength & Acceleration

A gravitational field causes masses inside it to experience a force of attraction (weight) and therefore accelerate.

g = 9.8 N.kg-1 or m.s-2

Force g = F/m

Gravitational field strength

= Gravitational Force per unit mass Each kilogram of mass experiences 9.8 N of force!

Accelerationg = F/m

Gravitational acceleration

= the rate at which a falling objects velocity increases

Falling objects fall 9.8 m.s-1 faster every second!

Mass & Weight Examples1. Calculate the weight of a 75 kg person.

2. What would your mass be if you weighed 600 N?

3. What is the mass of an object which weighs 1 N?

4. Calculate the weight of the following:

a) a 500 g tub of margerine

b) 0.2 g of sodium chloride

c) 250 ml of water

d) A 300 mg gold nugget

5. What is the gravitational acceleration on a planet where a 50 kg object has a mass of 250 N?

6. What is the gravitational field strength if an object weighing 400N has a mass of 10 kg.

7. If a 4 kg object falls on a planet and gains 30 m.s-1 every 2s then calculate its weight.

Newton's Universal Law of Gravitation

The force of gravitational attraction that exists between two masses m1 & m2 is given by

d - is the distance of separation between their centres.

m1 m2

d

Relationship between Force, mass and distance.

re

Fg = G m1∙ m2

r2

Me = mass of the earth re = distance between centres as

object so small!

Mass of Object = mo

Fg = G me∙ mo

re2

Fg = mo∙ g (N 2)

But since

mo∙ g = G me∙ mo

re2

g = G me

re2

Gravitational acceleration and Newton

Gravitational Field Strength

Calculate the weight of a 5kg bag of sugar on each planet shown.

g = 9.8 N.kg-1 g = 3.8 N.kg-1

A gravitational field causes masses inside it to experience a force of attraction.

Gravitational field strength = Gravitational Force per unit mass

g = F/m (N.kg-1)

g = 23.6 N.kg-1

5kg 5kg......N

......N 5kg.......N

Mass & Weight Calculate the missing values in each of

the following examples.

OBJECT MASS (kg) WEIGHT

Shoe 0.5

Pen

Newton’s gravitation examples1. Calculate the mass of the earth using the accepted

value for g (9.8 m.s-2) and the radius of the earth 6378.1 km.

2. What would your mass be on the moon?

3. The international space station which orbits at an average height of 350 km. a) Calculate your “weight” (w.r.t earth) on the

space station.b) Why would you feel weightless?

4. Calculate your weight on the planet Jupiter which has a mass of 1.8987 × 1027 kilograms and a diameter of about 142984 km.

5. Calculate the mass of an earth size planet on which a 50 kg person would have a weight of 1000 N.