Question

1.Zero, a hypothetical planet, has a mass of 4.9 x 1023 kg, a radius of 3.3 x 106 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0 x 107 J, what will be its kinetic energy when it is 4.0 x 106 m from the center of Zero? (b) If the probe is to achieve a maximum distance of 8.0 x 106 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?

2.In deep space, sphere A of mass 100 kg is located at the origin of an x axis and sphere B of mass 43 kg is located on the axis at x = 1.7 m. Sphere B is released from rest while sphere A is held at the origin. (a) What is the gravitational potential energy of the two-sphere system just as B is released? (b) What is the kinetic energy of B when it has moved 1.0 m toward A?

3.A satellite is placed in a circular orbit about Earth with a radius equal to 24% the radius of the Moon's orbit. What is its period of revolution in lunar months? (A lunar month is the period of revolution of the Moon.)

4.A 19.0 kg satellite has a circular orbit with a period of 3.70 h and a radius of 6.50 × 106 m around a planet of unknown mass. If the magnitude of the gravitational acceleration on the surface of the planet is 2.20 m/s2, what is the radius of the planet?

5.A satellite of mass 281 kg is in a circular orbit of radius 6.79 x106 m around a planet. If the period is 8090 s, what is the mechanical energy of the satellite?

6.A planet requires 320 (Earth) days to complete its circular orbit around its sun, which has a mass of 5.0 x 1030 kg. What are the planet's (a) orbital radius and (b) orbital speed?

Answer #1

*1. Given,*

*The mass of zero, M = 4.9 x 10 ^{23} kg*

*The radius of zero, R = 3.3 x 10 ^{6} m*

*The mass of a probe, m = 10 kg*

*(a)*

*Given, r = 4 x 10 ^{6} m*

*By using conservation of energy*

*Gravitational PE at surface + KE at surface = Gravitational
PE + KE at the given point*

*- GMm/R + KE = - GMm/r + KE*

*- (6.67 x 10 ^{-11}) ( 4.9 x 10^{23} ) (10) /
(3.3 x 10^{6} ) + 5 x 10^{7}= - (6.67 x
10^{-11}) (4.9 x 10^{23} ) (10) / (4 x
10^{6} ) + KE*

*K.E = (1 / (3.3 x 10 ^{6} )) - (1 / (4 x
10^{6} )) + 5 x 10^{7}*

^{ } = 5 x 10^{7} J

*(b)*

*By using the conservation of energy*

*Gravitational PE at surface + KE at surface = Gravitational
PE at the given point*

*- GMm/R + KE = - GMm/r + KE*

*- (6.67 x 10 ^{-11}) (4.9 x 10^{23} )
(10)/(3.3 x 10^{6} ) + KE = - (6.67 x 10^{-11})
(4.9 x 10^{23} ) (10)/(8 x 10^{6} )*

*K.E = 7.01 x 10 ^{7} J*

Zero, a hypothetical planet, has a mass of 4.9 x 1023
kg, a radius of 2.8 x 106 m, and no atmosphere. A 10 kg
space probe is to be launched vertically from its surface.
(a) If the probe is launched with an initial
kinetic energy of 5.0 x 107 J, what will be its kinetic
energy when it is 4.0 x 106 m from the center of Zero?
(b) If the probe is to achieve a maximum distance
of...

Zero, a hypothetical planet, has a mass of 6.0 x 1023
kg, a radius of 3.4 x 106 m, and no atmosphere. A 10 kg
space probe is to be launched vertically from its surface.
(a) If the probe is launched with an initial
kinetic energy of 5.0 x 107 J, what will be its kinetic
energy when it is 4.0 x 106 m from the center of Zero?
(b) If the probe is to achieve a maximum distance
of...

Zero, a hypothetical planet, has a mass of 5.8 x 1023
kg, a radius of 3.4 x 106 m, and no atmosphere. A 10 kg
space probe is to be launched vertically from its surface.
(a) If the probe is launched with an initial
kinetic energy of 5.0 x 107 J, what will be its kinetic
energy when it is 4.0 x 106 m from the center of Zero?
(b) If the probe is to achieve a maximum distance
of...

Zero, a hypothetical planet, has a mass of 4.5 x 1023 kg, a
radius of 3.4 x 106 m, and no atmosphere. A 10 kg space probe is to
be launched vertically from its surface. (a) If the probe is
launched with an initial kinetic energy of 5.0 x 107 J, what will
be its kinetic energy when it is 4.0 x 106 m from the center of
Zero? (b) If the probe is to achieve a maximum distance of...

A satellite of mass 1525 kg is in circular orbit around Earth.
The radius of the orbit of the satellite is equal to 1.5 times the
radius of Earth (RE = 6.378*106 m, ME = 5.98*1024 kg, G =
6.67*10-11 Nm2/kg2). (a) Find the orbital period of the satellite?
(b) Find the orbital (tangential) velocity of the
satellite. (c) Find the total energy of the
satellite?

Satellite X, a small moon of Planet X, has an orbital period of
1.77 days and an orbital radius of 4.22 x 10^5 km.
a) What is the mass of Planet X?
b) Assume that Satellite X moves in a circular orbit. What is
its orbital speed?
c) A small mass of m = 2.5 kg is dropped from rest from the
moon. What is its speed when it reaches the surface of Planet X,
whose radius is 71,492 km?...

A satellite has a mass of 5966 kg and is in a circular orbit
4.12 × 105 m above the surface of a planet. The period
of the orbit is 1.9 hours. The radius of the planet is 4.58 ×
106 m. What would be the true weight of the satellite if
it were at rest on the planet’s surface?

A satellite has a mass of 6495 kg and is in a circular orbit
4.94 × 105 m above the surface of a planet. The period
of the orbit is 2.2 hours. The radius of the planet is 4.19 ×
106 m. What would be the true weight of the satellite if
it were at rest on the planet’s surface?

A satellite has a mass of 6277 kg and is in a circular orbit
4.53 × 105 m above the surface of a planet. The period
of the orbit is 1.9 hours. The radius of the planet is 4.69 ×
106 m. What would be the true weight of the satellite if
it were at rest on the planet’s surface?

A satellite has a mass of 6372 kg and is in a circular orbit
4.05 × 105 m above the surface of a planet. The period
of the orbit is 2.1 hours. The radius of the planet is 4.41 ×
106 m. What would be the true weight of the satellite if
it were at rest on the planet’s surface?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 11 minutes ago

asked 16 minutes ago

asked 26 minutes ago

asked 36 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago