Students intend to use a cart-spring system study motion . A vertical plate with negligible mass is attached to a horizontal spring of spring constant k. When the spring is at its relaxed length , the plate is at position D as indicated in Figure 1 above. A cart is glued to the plate. The cart is initially held so that the spring is compressed as shown in Figure 2 above. The maximum force the glue can exert is F max Assume friction is negligible. The students plan to release the cart from rest so that the cart oscillates. They discuss whether the cart could detach from the plate during the cart's motion if the glue is not strong enough One student makes the following claim "The cart could never detach from the plate because the cart and the plate exert equal and opposite forces on each other so the forces on the cart add to zero. (a) Which underlined phrase or phrases are correct if either? If neither phrase is correct write " none." (b) Which underlined phrase or phrases are incorrect if either? If neither phrase is incorrect write "none." The cart is removed, and the plate is coated with very strong glue. The cart rolls to the right with positive velocity v cart , collides with and sticks to the plate, and then oscillates back and forth at the end of the spring. The graph above shows the velocity of the cart as a function of time after it has completed several oscillations. (c) Explain how this graph could be used to find the maximum compression of the spring as it oscillates. (d) The plate of negligible mass is replaced with a plate with mass similar to the cart's mass, and the collision is repeated. Again, the cart moves with velocity v cart collides with and sticks to the plate, and oscillates back and forth. In a clear, coherent paragraph-length response, explain how a graph of the cart's velocity as a function of time would differ from the one shown above if the plate's mass were not negligible. Provide a physical reason why each difference would occur.​