Question

physics gravity question

Answer 1

Prove that bodies accelerate (due to gravity) at a constant rate which we will call 'g'.

Answer 2

Now we can do an empirical proof, do an experiment outside and drop balls

Answer 3

we need heavy objects not effected by air resistence.

Answer 4

We can use a photographic still camera (and measure the frames, etc ).
But it is interesting that 'g' can be derived from newtons 2nd law and newtons law of universal gravitation.

Answer 5

THis is what i mean about what's 'important'. THese two laws are very important. ok lets do a review

Answer 6

2nd law of newton. anytime an object undergoes an acceleration, there is a force. THe acceleration is proportional to the force (more force more acceleration), and inversely proportional to mass (more mass less acceleration).

Answer 7

a = F / m

Answer 8

right

Answer 9

newtons universal law of gravitation:
newton found a formula that related two masses , he posited there is always a force of attraction between two masses.

the force between two masses ;
F = G*M*m/R^2

Answer 10

you could say the force is proportional to the product of the masses and inversely proportional the square of the distance. thats where the G comes in (constant of proportionality)

Answer 11

ok so far?

Answer 12

I know all this :)

Answer 13

so we have two equations so far

F = m*a
F = GM*m/R^2

Answer 14

ok at the surface of earth we have
m*a = GM*m/R^2 ,

Answer 15

it is similar for an electric charge among 2 charges

Answer 16

so a = GM/R^2 (canceling the m's)

Answer 17

these are all constants, G is universal constant of gravity, M is mass of earth, R is radius of earth

Answer 18

so we just call this 'g' ,

g = GM/R^2

Answer 19

it comes out to be about 9.8 m/s^2

Answer 20

now lets derive an equation for force at height x above the surface of the earth

Answer 21

err, i mean acceleration .

Answer 22

can you find a general formula for acceleration?

Answer 23

@timo86m , at a height x(t) , what is the acceleration due to gravity . we can assume that the object is at some height above the surface of the earth at time t

Answer 24

earth is so big u can safely assume that 10 m/s^2 at any height.

Answer 25

not for rockets or spaceships

Answer 26

unless you shooting a precision rocket.

Answer 27

its really easy, i will show you

Answer 28

there is a map on my txt book for all the Gs on earth.