Conceptual questions for dynamics of orbital motion: Gravitational and Coulomb forces

Fig. 1. Orbital motion of mass m around mass M at a radius r

A.  Gravitational Force.  Choose the word or phrase inside the parenthesis that makes the statement true. Write your answer on the space provided before each number.

1. According to Newton’s law of Gravitation, the gravitational force between two objects is directly proportional to the (sum, product) of their masses
2. and inversely proportional to the (distance, square of the distance) between them.
3. Thus, if one of the masses becomes twice that of the other mass, then the gravitational force is (2, 3)  times the force when the masses are the same.
4. On the other hand, if the distance between the masses is halved, the force between the masses is (1/2, 1, 2, 4) times the original force.
5. Now the gravitational force is (attactive, repulsive),
6. so that the force on mass m due to mass M points  (up, down, left, right).
7. This force is (centripetal, centrifugal).
8. By Newton’s (First, Second, Third) Law of Motion, the acceleration of mass m points (away, toward) mass M.
9. This acceleration is proportional to the (speed, square of the speed) of mass m
10. and inversely proportional to the (distance, square of the distance).
11. If the mass m is orbiting in a counterclockwise motion, then at point A, the velocity of mass m is pointing (up, down, left, right).
12. The orbital speed of the mass m is (), where is the mass’s orbital period.

B.  Coulomb Force.  Choose the word or phrase inside the parenthesis that makes the statement true. Write your answer on the space provided before each number.

1. The Coulomb force between two objects is proportional to the (sum, product) of the charges
2. and inversely proportional to the (distance, square of the distance) between them.
3. In a hydrogen atom, the mass M represents the proton with (negative, positive) charge
4. and mass m represents the electron with (negative, positive) charge.
5. Since the magnitude of the charges of the electron and proton are the same, then the force between the electron and the proton is (attractive, zero, repulsive).
6. Thus, when the electron is at point B, the force of the proton on the electron points (up, down, left right),
7. while the force of the electron on the proton points (up, down, left, right),
8. by Newton’s (First, Second, Third) law of motion.
9. If the electron is replaced by a proton, then the force between the two protons is (repulsive, attractive).
10. If the central proton is fixed in space, then an incoming electron would move in a (linear, parabolic, circular, hyperbolic) motion.
11. This is the principle behind (Coulomb’s, Rutherford’s) alpha particle scattering experiment to probe the structure of the atom.
12. On the other hand, the force between the proton and the neutron is (repulsive, zero, attractive).
13. So if the proton is fixed in space, then an incoming neutron would move in a (linear, parabolic, circular, hyperbolic) motion.
14. Inside the nucleus of an heavy atoms are several protons and neutrons.  By Coulomb’s law, the nucleus will (be stable, split).
15. Thus, there must be a nuclear force that is (stronger, weaker) than the Coulomb force in order to keep the nucleus intact.

Conceptual questions for a mass sliding on an inclined plane

by Quirino Sugon Jr.

Fig. 1. Mass on top of an inclined plane

Choose a word or phrase inside the parenthesis that makes the statement true.  Write your answer on the space provided before each number.

1. Gravitational force on an object on the plane is pointing (down, up).
2. By Newton’s (First, Second, Third) Law,
3. the normal force on the object is pointing (parallel, perpendicular) to the inclined plane.
4. If we assume that the object is only moving along the plane and the angle of inclination of the plane is with respect to the horizontal, then the magnitude of the normal force on the object is .
5. Since the only force acting on the object is (parallel, perpendicular) to the inclined plane,
6. then by Newton’s (First, Second, Third)
7. the acceleration of the object is (parallel, perpendicular) to the inclined plane.
8. Specifically, since the net force on the object is (down, up) the plane,
9. then the acceleration of the object is therefore (down, up) the plane.
10. The magnitude of the acceleration is ().
11. One way to check your answer is to make the inclined plane perpendicular to the ground, so that is ().
12. This gives an acceleration of magnitude ().
13. The other way to check your answer is to make the inclined plane parallel to the ground, so that is (.
14. This gives an acceleration of .
15. This means that if the object is initially at rest, then the object will (remain at rest, move with constant velocity, accelerate)
16. by Newton’s (First, Second, Third)  law.