Systems and Center of Mass AP Physics C Mechanics MCQ – Exam Style Questions etc.
Systems and Center of Mass AP Physics C Mechanics MCQ
Unit 2: Force and Translational Dynamics
Weightage : 20-15%
Question
In order to model the motion of an extinct ape, scientists measure its hand and arm bones. From shoulder to wrist, the arm bones are 0.60 m long and their mass is 4.0 kg. From wrist to the tip of
the fingers, the hand bones are 0.10 m long and their mass is 1.0 kg. In the model above, each bone is assumed to have a uniform density.
When the arm and hand hang straight down, the distance from the shoulder to the center of mass of the arm-hand system is most nearly
(A) 0.25 m
(B) 0.35 m
(C) 0.37 m
(D) 0.50 m
(E) 0.93 m
Answer/Explanation
Ans:C
Question
A meterstick of nonnegligible mass m is pivoted at its center, as shown. Two blocks, block 1 and block 2, are placed on top of the meterstick. When the meterstick is released from the rest at the position shown, it begins to rotate clockwise. Which of the following statements about the masses of the two blocks is correct?
(A) It cannot be determined which block has greater mass, because the lever arms associated with the torques provided by each block are different.
(B) The blocks are of equal mass, because the magnitude of the angular acceleration of each block is the same.
(C) Block 1 has greater mass, because the lever arm associated with the torque it provides is larger than that of block 2.
(D) Block 2 has greater mass, because more torque is provided by block 2 with a smaller lever arm.
(E) The blocks are of equal mass, because the meterstick’s mass is not negligible.
Answer/Explanation
Ans:
D—Because the pivot is at the meterstick’s center of mass, the meterstick’s weight provides no torque. The angular acceleration is clockwise; thus, clockwise torques are greater than counterclockwise torques. These torques are equal to the weight of each object times the object’s distance from the pivot. Object 2 provides a greater torque, yet its lever arm (the distance from the pivot) is smaller. Thus, object 2 must be more massive.
Question
Three objects, of mass 2 kg, 2 kg, and 4 kg, are arranged as shown in the diagram. Which of the following is closest to the y-coordinate of the three objects’ center of mass?
(A) 2.0 cm
(B) 3.5 cm
(C) 1.5 cm
(D) 0.5 cm
(E) 1.0 cm
Answer/Explanation
Ans:
E—Ignore the x direction entirely. In the y direction, there’s 4 kg at y = 0 and 4 kg at y = 2 cm. These equal masses have a center of mass directly in between, at y = 1 cm.
Question
A projectile is launched on level ground in a parabolic path so that its range would normally be 500 m. When the projectile is at the peak of its flight, the projectile breaks into two pieces of equal mass. One of these pieces falls straight down, with no further horizontal motion. How far away from the launch point does the other piece land?
(A) 250 m
(B) 375 m
(C) 500 m
(D) 750 m
(E) 1000 m
Answer/Explanation
Ans:
D—The center of mass of the projectile must maintain the projectile path and land 500 m from the launch point. The first half of the projectile fell straight down from the peak of its flight, which is halfway to the maximum range, or 250 m from the launch point. So the second half of equal mass must be 250 m beyond the center of mass upon hitting the ground, or 750 m from the launch point.