revision questions~ (1 Viewer)

[risaka]

my physics half yearly exam is in 3 days time need some quick help with some questions:

1. Newton tested his inverse square law of gravitation by using it to compare the gravitational and centripetal force acceleration of the moon in its orbit about the earth.
(i) The moon is 60 earth radii from centre of the earth. Calculate the gravitational acceleration of the moon towards the earth
(ii) How did newton calculate the centripetal acceleration of the moon? - formula

2. Saturn has 100 times the mass of the earth and is 10 times further away from the sun than the earth is.
(i)show that the forces exerted by the sun on saturn and on the Earth have the same magnitude.
(ii)Will saturn and earth have the same period of rotation about the sun? - in terms of kepler's law

3. A certain star is 10 light years from Earth. A spaceship leaves Earth at a speed of 0.8c to travel to the star. How long will the trip take
(i) as measured by the crew of the ship
(ii) observers on earth

thanks in advance ≧_≦""

 

[Mountain.Dew]

my physics half yearly exam is in 3 days time need some quick help with some questions:

1. Newton tested his inverse square law of gravitation by using it to compare the gravitational and centripetal force acceleration of the moon in its orbit about the earth.
(i) The moon is 60 earth radii from centre of the earth. Calculate the gravitational acceleration of the moon towards the earth
(ii) How did newton calculate the centripetal acceleration of the moon? - formula

thanks in advance ≧_≦""

all these questions are a simple application of formulae.

1)
(i) now, we use the formulae: F = Gm1m2/r^2...but not just yet...

change m1 --> mE, mE = mass of earth, and m2 --> mO, where mO = mass of moon.

so, since F = ma, THEN:

mOa = GmEmO/r^2 ==> a = GmE/r^2 <-- we use this formula, since we want the acceleration of a certain object (this case, the moon) towards earth, at a certain distance away.

so, simple plug in r = 60 earth radii = 60 * (some figure - look up in datasheet), the value for mE (also on data sheet), and G (ALSO on data sheet), and u obtain ur answer.

(ii) realise that for planets in orbit, the GRAVITATIONAL force from earth to the moon IS EXACTLY the CENTRIPETAL force of the moon to earth...therefore, since MASS is constant, the GRAVITATIONAL ACCELERATION from earth to moon is the same as the CENTRIPETAL ACCELERATION of the moon to earth.

more to come!

 

[Mountain.Dew]

2. Saturn has 100 times the mass of the earth and is 10 times further away from the sun than the earth is.
(i)show that the forces exerted by the sun on saturn and on the Earth have the same magnitude.
(ii)Will saturn and earth have the same period of rotation about the sun? - in terms of kepler's law

okay...consider F = GmSmP/r^2, where mS = mass of sun, mP = mass of planet in question, r = distance between the centre of masses.

simply plug in values for G, the mass of sun, mass of earth and their distances away into one equation to obtain a value for F*...and do the same for Saturn, to obtain a value for F^ --> realise that F* and F^ are the same.

(ii) simple application of Kepler's 3rd Law ==> get period as the subject of the equation, and plug in values ==> if both periods are the same, for Earth and Saturn, then the answer is YES...otherwise, NO. i tend to lean on the 'NO' side. my reasoning - think of Kepler's Law of Areas

3. A certain star is 10 light years from Earth. A spaceship leaves Earth at a speed of 0.8c to travel to the star. How long will the trip take
(i) as measured by the crew of the ship
(ii) observers on earth

(i) there is no 'relativity' application here, since the time is OBSERVED by the crew of the ship, NOT some STATIONARY point of reference. simply t = d/s ==> time it takes = 10 light years / 0.8c = some value, in years

(ii) now that u have the time of flight in years from (i), time to apply it to the time dilation equation ==> plug the value into t_o and v = 0.8c to obtain t_v, the time taken for the trip as observed from an inert point of reference on earth.

hope it helps, M.D.

 

[risaka]

thanks alot~~ deeply appreciate it