gravity form 4

SUHAILA MOHAMED NOR ADILAH SITI SARAH SYAZWANI ROSLAN

Gravity• A Universal Force

a)Until 17th century, - a heavy object would fall faster than a light object as Aristotle once taught.b)After research by Galileo Galilei - if air resistance can be ignored, all bodies fall with an equal acceleration.

1. Newton- studied the force of gravity. He got the inspiration when apple fell from a tree, hitting his head.

2. In Newton’s opinion, the falling apple was acted on by a force of attraction (i.e. the force of attraction due to gravity from the centre of the earth)

3. Any object which falls only under the influence of the force of attraction due to gravity and without any influence of other forces is said to experience free fall.

4. All object which experience free fall will fall with the same acceleration

(i.e. the acceleration due to gravity)

Gravitational Field1. The force of gravity acts through space and can

cause a body which is not in contact with any surface to fall freely to the ground – the earth is surrounded by a gravitational field which exerts a force on any body in the field.

2. The strength of a gravitational field – the gravitational force acting per unit mass on an object in the field. It is denoted by the symbol ‘g’

3. On the earth, the gravitational field strength, g is 9.8 N kg-1

4. Gravitational field strength: g = Gravitational force, F Mass of body, M

The non-uniform gravitational field of theEarth, g is represented by radial lines directed towards the centre of the earth.The field is strongest where the lines are close.

Example

Question :• A body of mass 2 kg has a weight of 20 N.

Find the value of the gravitational field strength

Solution:

g = 20 N = 10 N kg-1

20 kg

Gravitational acceleration

Mass , m Weight , w

The amount of matter in the object. definition

The force of gravity on the object.

The mass of an object is constant

everywhere.Changing of value

Varies with the magnitude of

gravitational field strength, g of the

location.

Scalar quantity Physical quantity Vector quantity

Base quantity Type of quantity Derived quantity

Kilogram, kg SI unit Newton, N

FORMULA

Force, F = ( mass, m ) ( acceleration, a )

Weight, w = ( mass, m ) ( gravitational acceleration, g )

Gravitational field strengh

Gravitational field = the region in which an object experiences a force due to gravitational attraction.

Gravitational field strength = the ratio of the weight to the mass of the object / weight per mass / W m

Rearrange the formula : W = ( m ) ( Gravitational field strength ) When compared to : W = ( m ) ( g )

so : g = Gravitational acceleration = Gravitational field strength

FREE FALLING OBJECT☻ Is an object falling

under the force of gravity only

☻ Does not encounter other force (example : air resistance or friction that would oppose its motion

The difference between a fall in air and a free fall in a vacuum of a coin and a

feather

Problem involving F = ma W = mg

Lift

When a girl stands on the platform of a

weighing scale, there are two forces acting on her :

When a girl stands on the platform of a

weighing scale, there are two forces acting on her :

a) The girl’s weight, w(=mg)Acting downwards

b) The upward normal reaction force, R exerted on her feet By the platform of the scale

The reading of the scale gives the value of the normal reaction Force, R

Different situation in the lift

Note : when the lift is accelerating upwards or downwards, the

reading on the scale gives the ‘apparent’ weight, which is equal

to the normal reaction force on the feet of the girl

QUESTIONS

A box of mass 1.6 kg is suspended from a spring balance hanging from the ceiling of a lift

What is the reading on the spring balace if :(a) The lift is stationary(b) The lift moves upwards at an acceleration

of 2 ms-2?(c) The lift moes downwards at an acceleration

of 3ms-2

[take g = 10 ms-2]

1

SOLUTION(a) If the lift is stationery : T = mg = 1.6 x 10 = 16 N(b) When the lift is accelerating upwards : T1 - mg = ma T1 = (1.6 x 10) + (1.6 x 2) = 19.2 N(c) When the lift is accelerating downwards : mg – T2 = ma T2 = (1.6 x 10) – (1.6 x 3) = 11.2 N

The weight of a student on earth’s is 450N. What is this weight on the moon if earth’s gravitational strength is six times the gravitational strength of the moon ?

2

SOLUTION (Symbol with subscript 1 represent the situation on

earth while symbols with subscript 2 represent the situation on the moon)

w1 = 450 N g1 = 6g w1 = mg w2 = mg w1 mg1 g1

w2 = mg2 = g2

w2 = w1g2 g1

= 450 x g2

6g2

= 75 N

A ball is thrown vertically upwards with an initial velocity of 20 ms-1. If g = 10 ms-2 and air resistance can be neglected, find:

(a) the maximum height reached (b) the time taken before it reaches

the ground

3

SOLUTIONa)The velocity of the ball is zero when it

reaches its maximum height. The acceleration of the ball when it is thrown upwards is -g as it experiences a deceleration

u = 20 ms-1 v = 0 a = -10 ms-2

v2 = u2 + 2as0 = 202 + 2(-10)ss = 400 m 20 = 20 m (maximum height reached = 20 m)

(b) The displacement of the ball on reaching the ground is zero

s = ut + 1 at2

20 = 20 t + 1 (-10)t2

2 5 t2 - 20 t = 05 t (t-4) = 0 t = 0 or 4

( time taken before it reaches the ground = 4 s)