Solution Found!
In discussing the two carts of Figure 11.1, I mentioned
Chapter 11, Problem 11.1(choose chapter or problem)
In discussing the two carts of Figure 11.1, I mentioned that it is simplest to assume that when the two carts are in equilibrium the lengths L 1, L2, L3 of the three springs are equal to their natural, unstretched lengths /1, /2, /3. However, this assumption is not needed, and the three springs could all be in tension (or compression) at the equilibrium position. (a) Find the relations among these six lengths (and the three spring constants k1, k2, k3) required for the two carts to be in equilibrium. (b) Show that the net force on either cart is exactly as given in Equation (11.2), irrespective of how L1, L2, L3 compare with /1, /2, /3, just as long as x1 and x2 are measured from the carts' equilibrium positions.
Questions & Answers
QUESTION:
In discussing the two carts of Figure 11.1, I mentioned that it is simplest to assume that when the two carts are in equilibrium the lengths L 1, L2, L3 of the three springs are equal to their natural, unstretched lengths /1, /2, /3. However, this assumption is not needed, and the three springs could all be in tension (or compression) at the equilibrium position. (a) Find the relations among these six lengths (and the three spring constants k1, k2, k3) required for the two carts to be in equilibrium. (b) Show that the net force on either cart is exactly as given in Equation (11.2), irrespective of how L1, L2, L3 compare with /1, /2, /3, just as long as x1 and x2 are measured from the carts' equilibrium positions.
ANSWER:Step 1 of 3
(a) When the two carts are in equilibrium, the tensions in the three springs must be equal.