2005 Question 6
(i) Define angular velocity.
Angular velocity is the rate of change of displacement with respect to time.
(ii) Define centripetal force.
The force - acting in towards the centre - required to keep an object moving in a circle is called
Centripetal Force.
(iii) State Newton’s Universal Law of Gravitation.
Newton’s Law of Gravitation states that any two point masses in the universe attract each other with a
force that is directly proportional to the product of their masses, and inversely proportional to the
square of the distance between them.
(iv) A satellite is in a circular orbit around the planet Saturn.
Derive the relationship between the period of the satellite, the mass of Saturn and the radius of
the orbit.
See notes on the Circular Motion chapter for a more detailed derivation.
(v) The period of the satellite is 380 hours. Calculate the radius of the satellite’s orbit around
Saturn.
T = 380 × 60 × 60 = 1.37 × 106 s
r3 = T2GM/4π2 r3 = (1.37 × 106)2(6.7 × 10–11)( 5.7 × 1026)/ 4π2 r = 1.2 × 109 m
(vi) The satellite transmits radio signals to earth. At a particular time the satellite is 1.2 × 1012 m
from earth. How long does it take the signal to travel to earth?
v = s/t
(3.0 × 108) = (1.2 × 1012)/t
t = 4000 s
(vii) It is noticed that the frequency of the received radio signal changes as the satellite orbits
Saturn. Explain why.
Doppler Effect due to relative motion between source of signal and the detector
2005 Question 12 (a)
(i) State the principle of conservation of energy.
Energy cannot be created or destroyed but it can only be changed from one form to another .
(ii) A basketball of mass 600 g which was resting on a hoop falls to the ground 3.05 m below.
What is the maximum kinetic energy of the ball as it falls?
KE = PE (at height of 3.05 m)
v2 = u2 +2as v2 = 0 + 2(9.8)(3.05) v2 = 59.78 {you could also have use P.E.
= mgh}
Ek = ½mv2 = ½ (0.60)(59.78) Ek = 17.9 J
(iii) On bouncing from the ground the ball loses 6 joules of energy. What happens to the energy lost
by the ball?
It changes into sound and heat.
(iv) Calculate the height of the first bounce of the ball.
[retained energy = 17.9 – 6] E = 11.9 J
E = mgh h = E / mg h = 11.9 /(0.600)(9.8) h = 2.02 m
