A graph shows the Force of a spring (y axis) against Displacement (x axis) in a linear function. An obvious point for the gradient is the point (0.5 metres, 140 Newtons). What is the spring constant and how much energy is stored in the spring when it is compressed by 0.5 metres? Hope the description helps. Hooke's law states: F=-kx Therefore: 140=-0.5k Therefore: k=-40/0.5=-80 (But I thought spring constant cannot be negative?) Also, no idea how to work out energy stored. Any help will be appreciated! Thanks
Welcome to physics forums. Don't forget that displacement, is a vector quantity - i.e. direction matters. In the usual set up, a spring is compressed when x < 0 (i.e. its length decreases). Therefore, if your spring is compressed by 0.5 meters, then x = -0.5. How is potential energy related to the force (in general)?
Thanks for the welcome! I see about displacement. (Forgot displacement is a vector quantity - sad face) About the potential energy, is potential energy the same as the work done? So in this case, the area bound by the line and the x axis from 0 to 0.5 metres?
This is one of those Newton's third law issues. If you are talking about the force you exert on the spring to stretch it a distance x, then the force is positive when the displacement is positive, and the force is negative when the displacement is negative. If you are talking about the force that the spring exerts on you when you stretch it a distance x, then the force is negative when the displacement is positive, and the force is positive when the displacement is negative.
Mathematics is a tool used by Physicist. We are not bound by it. It does help us to predict what should be the case. Hooke's law describes the relationship between the restoring force of the spring, as experienced by the agent stretching the spring, and the change in length of the spring. The negative sign in this law serves to indicate that the direction of the restoring force and the change in length is in opposite directions. The spring constant is therefore positive - no sense in having a negative constant! If you want to use Hooke's law to calculate the constant you need to take the directions into account.