Errata for Conservation Laws TG

Activity 74, p. 513, question B3, part (c) answer

  • In the second paragraph, the area of each 'box' is wrong. It should be 0.01N-s, i.e., "... and each box has an area of (2N) x (0.005s) = 0.01N-s..."

Activity 76, p. 529, question A3 answer

  • The parts are not labeled, i.e., the "(a)", "(b)", and "(c)" labels are missing.

Activity 76, p. 532

  • The answers and comments to questions R1, R2, and R3 are missing.
  • The answer for R1 is, "Total momentum is conserved for situations A3 and A6. It is zero initially, and remains the same throughout the time interval specified. Total momentum is approximately conserved for situation A1, because the impulse delivered to the system by gravitation is small during the explosion. At least one component of the total momentum is conserved for the other 5 situations. We define the x-direction to be the horizontal in the plane of the page (i.e., to the right), the y-direction to be the vertical, and the z-direction to be the horizontal perpendicular to the plane of the page (i.e., directly toward you). In situations A2, A4, and A7, the net external force is in the y-direction, so total momentum is conserved in the x- and z-directions. In situation A5, the net external force has y- and z-components, so momentum is conserved only in the x-direction."
  • The comments for R1 are:
    • Students might think that momentum is not conserved in situation A6, because the wheel is slowing down.
    • Students might consider only the ball in A3, rather than the Earth-ball system.
    • In situation A3, students might not ignore the gravitational forces exerted on the Earth-ball system by the Sun, the Moon, and the planets.
    • Students might not recognize that the total momentum of the Earth-ball system is staying the same during the motion of the ball.
    • Students might only consider two directions, i.e., the x- and y-directions.
    • In situation A5, we are assuming that the bow string exerts a force on the arrow in the yz-plane.
    • Students might think that momentum is not conserved in any direction in situation A7, because the ball's are going in all directions.
  • The answer for R2 is, "In situations A3 and A6, all forces are internal; the net force on each system is zero."
  • The comments for R2 are:
    • If students do not have the correct set of situations here, they are likely to generalize improperly.
    • Students might not realize that in A3 they are expected to ignore the forces exerted by the Sun, the Moon, and the other planets.
    • Students might not realize that in A6 the net force on the wheel is zero, because it is slowing down.
  • The answer to R3 is, "For those situations in which momentum is not conserved, there are external forces on the specified system. In each case, the direction of the change in momentum is the same as the direction of the net external force. In order to always conserve momentum, it is necessary to choose a system large enough so that there are no external forces on it. If we include the Earth in each system and ignore the gravitational forces exerted by the Sun, the Moon, and the planets, then momentum is conserved in all the situations."
  • (There are no comments for R3 at this time.)

Activity 83, p. 584, question A1 answer

  • The explanation (column 5) should read, "Monkey exerts F__N_1 and _Ffs. Whatever is holding up the rope exerts _F__N_2 (assuming, e.g., that the rope is tied to a hook in the ceiling). The displacement of the rope is zero."

Activity 87, p. 616, "Anticipated Difficulties for Students", bullet 7 (i.e., last bullet)

  • The 'clay' should be a 'cart', i.e., "Analyzing the cart in situation R3... because the work done on the cart is done..."

Activity 87, p. 618, "Providing Support to Ensure Student Progress", bullet 6 (i.e., next to last bullet)

  • Change to: "In situation R3, focus students attention on forces that are applied through a displacement, such as forces internal to the spring, rather than forces that are applied through zero displacement, such as the normal force exerted by the wall."

Activity 87, p. 620, question A3(b) answer

  • The explanation is wrong, because we do not know how to calculate the work done by friction, as described in the Reader. Therefore, students are expected simply to use common sense to try to answer this question. Later, the explanation will be that there is a loss of energy from the macroscopic realm to the microscopic realm, which means that the speed must be smaller after hitting the spring than before.

Activity 87, p. 620, question A3(b) bullet

  • The comment is inappropriate for the same reason that the explanation is inappropriate, that is we do not know how to calculate the work done by friction, as described in the Reader. It should read, "The work done by the friction force on the cart cannot be calculated or even estimated. Further, knowing its value would be of no consequence here, because all of the macroscopic kinetic energy lost by the cart becomes microscopic energy of the cart. In other words, the forces are internal to the cart, so the energy remains with the cart. However, at this point in the course, students are not expected to be able to make this distinction between macroscopic and microscopic energy."

Many thanks to Lonnie Grimes of Oakmont High School in Roseville, CA, who found almost all of these mistakes.