Purchase Solution

Two spring system

Not what you're looking for?

Ask Custom Question

The ends of two identical springs are connected. Their unstretched lengths l are negligibly small and each has spring constant k. After being connected, both springs are stretched an amount L and their free ends are anchored at y = 0 and x = +/- L as shown (see attachment). The point where the springs are connected to each other is now pulled to the position (x , y). Assume that (x , y) lies in the first quadrant.

A. What is the potential energy of the two-spring system after the point of connection has been moved to position (x , y)? Keep in mind that the unstretched length l of each spring is much less than L and can be ignored (i.e., l << L).
Express the potential in terms of k, x, y, and L.

B. Find the force F on the junction point, the point where the two springs are attached to each other.
Express F as a vector in terms of the unit vectors x and y.

Purchase this Solution

Solution Summary

The potential energy of the two-spring systems are examined. The force on the junction point are determined.

Solution Preview

Point C is the (x,y) point. We have to determine the lengths of the two springs in the given configuration.
Length of spring 1 = BC = √(L-x)2+y2
Length of spring 2 = CA = √(L+x)2+y2

Part A : Potential energy stored in a spring = ½ kd2 where d is the extension/compression of spring (change in length from its normal length). In the present case as the normal length is negligible as compared to the extended length, d ...

Purchase this Solution

Free BrainMass Quizzes
Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.

Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.

Intro to the Physics Waves

Some short-answer questions involving the basic vocabulary of string, sound, and water waves.

Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.

The Moon

Test your knowledge of moon phases and movement.