Question 1: An astronomer discovers a planet with two moons. One moon is 2 times as far from the center of the planet as the other and 3 times the mass of the other moon. What is the ratio of the gravitational force on the first moon to the gravitational force on the second moon? (A) 0.33 (B) 0.40 (C) 0.66 (D) 0.75 (E) 0.90 Question 2: A 1newton force and a 4newton force act in opposite directions. What is the magnitude of the resultant force, in newtons? (A) 0 (B) 1 (C) 3 (D) 4 (E) 5 Question 3: An object starts from rest and accelerates at 6.0 m/s^2 for 4.0 seconds. How far does it travel? (A) 8.0 m (B) 12 m (C) 48 m (D) 96 m (E) 288 m Question 4: Force A and Force B act on an object. Let theta equal the angle between the directions of the two forces. At what value of theta is the resultant force the greatest? (A) 0 deg (B) 45 deg (C) 60 deg (D) 90 deg (E) 180 deg Answers:1 (D) The force is directly proportional to the masses and indirectly proportional to the square of the distances. This results in a ratio of 3/4, or 0.75. 2 (C) Because the forces act in opposite directions, the magnitude of the resultant force is the difference in them. The direction is in the direction of the greater force. 3 (C) delta x = vel_initial . delta t + (1/2) acc . (delta t)^2 = 0 + (1/2) (6 m/s^2) (4 s)^2 = 48m. 4 (A)
The resultant force is greatest when the magnitudes of the two forces combine. This occurs when they act in the same direction and, therefore, have an angle of 0 deg between them.
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