# Block on an inclined plane between two strings

• paulius005
In summary, the conversation discusses a block of mass M resting on an inclined plane with two springs connected to it and two posts. The top spring is stretched by 0.082 m and the bottom spring is compressed by the same amount. With the given values of M = 0.25 kg and θ = 30o, the spring constant of the bottom spring, k, can be found by equating the potential energy stored in the springs to the work done by the gravitational force on the block. This leads to the equation mgsin(theta)=3k, where m is the mass of the block and g is the acceleration due to gravity. By solving for k, the spring constant of the bottom spring can be determined.

#### paulius005

Block of mass M between two strings on incline?
A block of mass M rests on a frictionless inclined plane of angle θ as shown in the diagram below. Two springs of equal length are connected to the block and to two posts as shown. The separation between the posts is equal to the sum of relaxed lengths of the springs and the length of the block.

Suppose the top spring is stretched from its relaxed length by an amount δx = 0.082 m and the bottom string is compressed by the same amount.. If the spring constant of the top spring is twice that of the bottom spring and M = 0.25 kg and θ = 30o, what is k, the spring constant of the bottom spring?

http://i43.tinypic.com/2z4bcaw.gif

Now I know that I may need to use F = -k(X-Xo) and draw a free body diagram.

After drawing the free body diagram I get that mgsin(theta)=3k since there is one spring with spring constant k and another with 2k. I am not sure how to put the stretched length into all that though. Or since -k(X-Xo) = the vector some of the forces does that mean that mgsin(theta) = 3(-k(X-Xo)). Just a bit confused.

Hi paulius005, welcome to PF.
What is the potential energy stored in the springs?
What is the work done by gravitational force on the block?
Equate them to find k.