Phys101
Term:122
Online HW-Ch13-Lec03
Q1:
A small satellite is in elliptical orbit around Earth as shown. Numbers 1 and 2 indicate two
positions of the satellite in its orbit. If L denotes the magnitude of its angular momentum and
K denotes kinetic energy of the satellite, which of the
following relations is TRUE?
A.
B.
C.
D.
E.
L2 > L1 and K2 > K1
L2 > L1 and K2 = K1
L2 = L1 and K2 = K1
L2 = L1 and K2 > K1
L2 < L1 and K2 = K1
Ans:
D, because the angular momentum is conserved (so L2 = L1), and the tangential speed is
larger at 2, so K2>K1.
Q2:
A planet is in circular orbit around the Sun. Its distance r p from the Sun is r p = 4r E ,
where r E is the average radial distance of Earth from the Sun. By what factor is the
year of the planet larger than Earth’s year? (Give your answer in three significant
figures form)
Ans:
TP 2 = �
4π2
4π2
� rp 3 ⇒ Tp = ��
�r 3
GMs
GMs p
and TE = ��
Now Tp = ��
4π2
� r 3 where Ms is the mass of sun and rp = 4rE
GMs E
4π2 3 3
4π2 3
� 4 rE = �43 ��
r � = √64 TE = 8TE ⇒ factor = 8.00
GMs
GM E
KFUPM-Physics Department
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Phys101
Term:122
Online HW-Ch13-Lec03
Q3:
A rock of unknown mass coming from outer space is heading
directly toward Earth. When the rock is at a distance of 9R E from the
Earth's surface, its speed is 12 km/s. Neglecting the effects of the
Earth's atmosphere (like air resistance) on the rock, find the speed of
the rock (in m/s) just before it hits the surface of Earth. Given the
radius and mass of Earth as R E = 6.370×106 m and M E = 5.98×1024
kg, respectively. (Give your answer in three significant figures form)
𝐀𝐧𝐬:
hi = 9R E ⟹ ri = hi + R E = 9R E + R E = 10R E ; vi = 12 × 103 m/s
hf = 0 ⇒ rf = hf + R E = 0 + R E = R E ; vf = ?
Conseravation of Mechanical Energy: k f + Uf = K i + Ui
⟹
1
GmME
1
GmM
1
1
GME GME
mvf 2 + �−
� = mvi 2 + �−
� ⟹ vf 2 = vi 2 −
+
2
rf
2
ri
2
2
ri
rf
vf = �vi 2 −
2GME 2GME
2GME 1
1
18GME
+
= �vi 2 −
� − � = �vi 2 +
10R E
RE
RE
10 1
10R E
(12 × 103 )2 + 18 × 6.67 × 10−11 × 5.98 × 1024
= �
= 160 × 102 m/s
10 × 6.37 × 106
KFUPM-Physics Department
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