Download 2013 Q6 - Loreto Balbriggan

State Examination Commission – Physics Higher Level, 2013
Question 6
(i) State Newton’s law of universal gravitation.
Textbook definitions
(ii) Explain what is meant by angular velocity. Derive an equation for the angular velocity of an object in terms of its
linear velocity when the object moves in a circle.
Angular velocity means the rate of change of angular displacement, ω = θ/t, measured in rad s-1.
ω= θ
t
s
but, θ=
r
s
so, ω= ,
rt
s
now, = v
t
v
Hence, ω=
r
The International Space Station (ISS), shown in the photograph, functions as a research laboratory and a location for
testing of equipment required for trips to the moon and to Mars. The ISS orbits the earth at an altitude of 4.13 × 10 5 m
every 92 minutes 50 seconds.
(iii) Calculate
(a) the angular velocity,
ω= θ
t
2π
ω=
(92×60)+50
−3
−1
ω=1.128×10 rad s
(b) the linear velocity, of the ISS.
v=rω
v = (6.37×106 +4.13×10 5)(1.128×10 −3)
−1
v = 7651 ms
(iv) Name the type of acceleration that the ISS experiences as it travels in a circular orbit around the earth. What force
provides this acceleration?
Centripetal acceleration.
Gravity.
(v) Calculate the attractive force between the earth and the ISS. Hence or otherwise, calculate the mass of the earth.
2
5
2
mv
4.5×10 ×7651
a) F =
=
=3.88×10 6 N
6
r
6.37×10 +4.13×105
GMm
b) However, F =
d2
−11
5
6.67×10 ×M ×4.5×10
3.88×10 6=
6
5 2
( 6.37×10 +4.13×10 )
24
M=5.95×10 kg
(vi) If the value of the acceleration due to gravity on the ISS is 8.63 m s−2, why do occupants of the ISS experience
apparent weightlessness?
Because both the ISS and the occupants experience the same acceleration towards the earth, and thus the occupants
appear weightless.
C. Garvey 2013
(vii) A geostationary communications satellite orbits the earth at a much higher altitude than the ISS. What is the period
of a geostationary communications satellite?
The same as the period of rotation of the earth, one day.
(mass of ISS = 4.5 × 105 kg; radius of the earth = 6.37 × 106 m)
C. Garvey 2013