How do I split a String and keep the delimiters?

Physics Question - Springs?

• I have lab tomorrow and before the lab we have to answer a bunch of warm-up questions. I could use some help on how to find the equation. Keep in mind I have absolutely no physics experience, and we have never talked about any of these topics in class yet. So basically I am just completely lost. There is a table with a spring in the center. Each end of the spring is attached to a string. Each string runs over a pulley on opposite ends of the table and there is a hanging object on each string (of equal weights). The other table has the same set up but the spring is only attached to one string and one hanging object. First answer the questions for the scenario with one hanging object: 1. What are the forces acting on the hanging object, the spring, and the strings? 2. Write the equation to express the condition in equilibrium for the hanging object, another equation for the spring and a third equation for the string. 3. Use Newton's third law to identify pairs of forces, acting on different objects, that must have equal magnitudes. 4. Write an equation that relates the extension of a spring to the force it exerts. Use this equation and the results of the previous steps to write down the relationship between the extension of the spring and the weight of the hanging object. Then do the same for the scenario with two hanging objects except determine the relationship between the extension of the spring and the weight of ONE of the hanging objects. How is the displacement of each hanging mass relation to the spring extension? Basically, I know you have to use Hooke's law. And the gravitational force equation. I have some stuff written down so far but basically I just need help. If there is equal weight pulling on the spring would it matter that its on one side or split...wouldn't the spring pull the same distance no matter what, as long as the weight pulling on it is the same? If you can help me I would appreciate it so much. I would contact my TA but he doesn't check his e-mail on the weekend. I've been trying to figure it out for so long and I feel like I'm just thinking in circles. Thank you!

• Answer:

  1. Gravity. the springs 'restoring force' 2. F = ma m = mass of object a = acceleration due to gravity F = -kx k = spring restoring force x = spring extension ma + kx = 0 3. As previously stated, ma = -kx equal magnitudes but opposite in direction. The total force is zero which is why nothing moves. 4. F = -kx. This is a linear equation so that twice the force is twice the extension etc. With two weights it's additive. i.e. F = (m1 + m2) * a = -kx John