B)Opposite in Direction to the Frictional Force Exerted on the Merry-Go-Round by the Person

B)Opposite in Direction to the Frictional Force Exerted on the Merry-Go-Round by the Person

  1. When a person stands on a rotating merry go-round, the frictional force exerted on the person by the merry-go-round is

A)greater in magnitude than the frictional force exerted on the person by the merry-go-round

B)opposite in direction to the frictional force exerted on the merry-go-round by the person

C)directed away from the center of the merry-go-round

D)zero if the rate of rotation is constant

E)independent of the person's mass

  1. Each of five satellites makes a circular orbit about an object that is much more massive than any of the satellites. The mass and orbital radius of each satellite are given below. Which satellite has the greatest speed?

Mass Radius

A)m R

B)m R

C)m R

D)m 2 R

E)2m R

  1. An asteroid moves in an elliptic orbit with the Sun at one focus as shown above. Which of the following quantities increases as the asteroid moves from point P in its orbit to point Q?

A)Speed

B)Angular momentum

C)Total energy

D)Kinetic energy

E)Potential energy

  1. Mars has a mass that of Earth and a diameter that of Earth. The acceleration of a falling body near the surface of Mars is most nearly

A) 0.25 m/s2

B) 0.5 m/s2

C) 2 m/s2

D) 4 m/s2

E)25 m/s2

  1. If Spacecraft X has twice the mass of Spacecraft Y. then true statements about X and Y include which of the following?

I. On Earth, X experiences twice the gravitational force that Y experiences.

II. On the Moon, X has twice the weight of Y.

III. When both are in the same circular orbit, X has twice the centripetal acceleration of Y.

A)I only

B)III only

C)I and II only

D)II and III on1y

E)I, II, and III

  1. The two spheres pictured above have equal densities and are subject only to their mutual gravitational attraction. Which of the following quantities must have the same magnitude for both spheres?

A)Acceleration

B)Velocity

C)Kinetic energy

D)Displacement from the center of mass

E)Gravitational force

  1. An object moves up and down the y-axis with an acceleration given as a function of time t by the expression , where A and  are constants. What is the period of this motion?

A)

B)

C)

D)

E)

8. A new planet is discovered that has twice the Earth’s mass and twice the Earth’s radius. On the surface of this new planet, a person who weighs 500N on Earth would experience a gravitational force of

a.125Nd.1000N

b.250Ne.2000N

c.500N

Answers:

  1. B; “Stands” is code for “not moving” or “at rest” which means the forces acting are in equilibrium. Newton’s 3rd Law applies.
  2. B; Generally, the smaller the orbital radius, the greater the speed. Need proof?

which simplifies to . Since both G and M are constants, the velocity is proportional to the square root of the radius, which is a term in the denominator. Answer B has the smallest radius, therefore it has the greatest velocity.

  1. E; The speed would slow since planets move fastest in that part of their orbit where they are closest to the Sun, which eliminates answer A). Angular momentum is proportional to mvr, so m is constant and as r increases, v decreases which offset a bit, so answer B) is not the best answer. Answer C) cannot be correct unless both D) and E) are correct which leaves us with deciding whether answers D) or E) are correct. Well, if velocity slows, then KE decreases rather than increases, leaving potential energy to increase, so E) is the best answer.

Need proof? Also , so as r increases the magnitude of U decreases, but since it is a negative quantity, the value becomes more positive which is an increase in potential energy.

  1. D; Recall , so gMars :gEarth =

5. C;

I. TRUE, the gravitational force is proportional to the mass of the spacecraft.

II. TRUE, the gravitational force is still proportional to the masses of the spacraft.

III. FALSE, , the mass of the satellite divides out, thus the acceleration is the same for both.

6.E; According to Newton’s Third Law, the gravitational force on both spheres is of equal magnitude.

7.D; ; this is simply the period of the mathematical function.

8.B; The relevant information is g = GM/R2 . If M is doubled, and R is also doubled, then

g/ = G(2M)/(2R)2 = (2/4) GM/R2 = g/2, so the new weight would be 500 N/2 = 250N.

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