Newton showed that all bodies attract one another by a force of gravity given by:

F= Gxm1m2/r^2

M1 and m2 are the masses in kg

R is the separation between the objects centre’s

G=6.67x10^-11 Nm^2kg^-2, the universal constant of gravity

Acceleration due to gravity

Near the surface of the planet the acceleration due to gravity is by equating the radius of the planet and the gravity on it.

W=Fgravity

Mg= Gm1m2/r^2

.:. g= Gm/Rp^2

Acceleration due to gravity is different at different locations on Earth due to:

1. Local changes in density of the earth’s crust

2. The earth is not a sphere, causing ‘g’ to be less at the equator because of the earths larger radius there

3. The rotation of the earth causes ‘g’ to be lower on the equator beause some centripetal force is needed there

PRAC: Projectile Motion

Aim: To verify the equations of projectile motion and Galileo’s assumption that the vertical and horizontal components of motion can be treated independently.

Method ptA:

Set up an inclined plane and roll a ball down it. For a rolling ball:

KEbottom= PEtop/2 or v=√gh (check that eqn gives the correct velocity of the ball)

ptB: Using three different heights for the inclined plane, calculate the velocity of the ball then use this velocity to find how far from the end of the table it would have landed (the range).

Place a cup the crrect distance and compare the balls calculated range to its experimental (measured) range.

1.2 Projectile Motion

Galileo showed that projectile motion could be described fully if the vertical and horizontal components of the motion were treated independently.

The initial velocity can be separated into vertical and horizontal components by treating it as the sum of vector components.

We can then use the equations of motion to describe each component of motion as follows:

Vertical:

y= 1/2gt^2 +UyT

Vy= gt+ Uy

Vy^2= 2Gy+ Uy^2

Horizontal:

Ux=Vx

X(displacement)= UxT...