PHYS 2211 Module 12 Self Assessment Practice Problems
Module 12 Self Assessment Practice Problems
12.1
Astrology makes much of the position of the planets at the moment of one’s birth. The only known force a planet exerts on Earth is gravitational.
(a) Calculate the gravitational force exerted on a 4.20-kg baby by a 100-kg father 0.200 m away at birth (he is assisting, so he is close to the child).
(b) Calculate the force on the baby due to Jupiter if it is at its closest distance to Earth, some 6.29 x 1011 m away. How does the force of Jupiter on the baby compare to the force of the father on the baby? Other objects in the room and the hospital building also exert similar gravitational forces. (Of course, there could be an unknown force acting, but scientists first need to be convinced that there is even an effect, much less that an unknown force causes it.)
Answer: (a) 7.01 x 10-7 N (b) 1.35 x 10-6 N
12.2
Asteroid Toutatis passed near Earth in 2006 at four times the distance to our Moon. This was the closest approach we will have until 2060.
(a) If it has mass of 5.0 x 1013 kg, what force did it exert on Earth at its closest approach?
(b) What was the acceleration of Earth caused by asteroid Toutatis at its closest approach?
(c) What was the acceleration of Toutatis at this point?
Answer: (a) 8.44 x 109 N (b) 1.41 x 10-15 m/s2 (c) 1.69 x 10-4 m/s2
12.3
(a) What is the acceleration due to gravity on the surface of the Moon?
(b) On the surface of Mars?
(c) Calculate the acceleration due to gravity on the surface of the Sun.
(d) By what factor would your weight increase if you could stand on the Sun? (Never mind that you cannot.)
On a planet whose radius is 1.2 x 107 m the acceleration due to gravity is 18 m/s2. What is the mass of the planet?
Answer: 3.9 x 1025 kg
12.5
An average-sized asteroid located 5.0 x 107 km from Earth with mass 2.0 x 1013 kg is detected headed directly toward Earth with speed of 2.0 km/s.
(a) What will its speed be just before it hits our atmosphere? (You may ignore the size of the asteroid.)
(b) What will be the kinetic energy of the asteroid just before it hits Earth?
(c) Compare this energy to the output of the largest fission bomb, 2100 TJ. What impact would this have on Earth?
Answer: (a) 7 km/s (b) 4.9 x 1020 J
12.6
Find the mass of Jupiter based on the fact that Io, its innermost moon, has an average orbital radius of 421,700 km and a period of 1.77 days.
Answer: 1.89 x 1027 kg
12.7
What is the escape speed of a satellite located at the Moon’s orbit about Earth? Assume the Moon is not nearby.
Answer: 1440 m/s
12.8
Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 x 1011 solar masses. A star orbiting on the galaxy’s periphery is about 6.0 x 104 light-years from its center.
(a) What should the orbital period of that star be?
(b) If its period is 6.0 x 107 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of other matter, such as a very massive black hole at the center of the Milky Way.
Answer: (a) 3.0 x 108 years (b) ~ 2 x 1013 solar masses
12.9
(a) Evaluate the gravitational potential energy between two 5.00-kg spherical steel balls separated by a center-to-center distance of 15.0 cm.
(b) Assuming that they are both initially at rest relative to each other in deep space, use conservation of energy to find how fast will they be traveling upon impact. Each sphere has a radius of 5.10 cm.
Answer: (a) 1.1 x 10-8 J (b) 3.2 x 10-5 m/s
12.10
Using the average distance of Earth from the Sun, and the orbital period of Earth,
(a) find the centripetal acceleration of Earth in its motion about the Sun.
(b) Compare this value to that of the centripetal acceleration at the equator due to Earth’s rotation.
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