How Do You Solve the Block and Spring Dynamics Problem?

[fireemblem13]

One of three blocks is attached to ceiling by a cord. Two others are connected by springs to the first block and to each other with coefficient k. What's the deformation of the springs? What's the tension in the cord? If the cord is cut, what's the acceleration of the blocks?

I'm somewhat clueless, so I'd appreciate a nudge in the right direction.

 

[JaWiB]

Start with free body diagrams for each block, then use Hooke's law to find the deformation in the springs (and the fact that the blocks are in static equilibrium, so F_net=0)

 

[kerimek]

The deformation of the springs can be calculated using Hooke's Law, which states that the deformation of a spring is directly proportional to the applied force. In this case, the force applied to the springs is the weight of the blocks, and the coefficient k represents the stiffness of the springs. Therefore, the deformation of the springs can be calculated by dividing the weight of the blocks by the stiffness of the springs.

The tension in the cord can be calculated by considering the forces acting on the first block. The tension in the cord will be equal to the sum of the forces acting on the block in the vertical direction. These forces include the weight of the block and the forces exerted by the springs. By setting up and solving equations using Newton's Second Law, the tension in the cord can be determined.

If the cord is cut, the blocks will experience an acceleration due to the force of gravity. This acceleration can be calculated by dividing the net force acting on the blocks (the weight of the blocks minus the tension in the cord) by the total mass of the blocks. This will give the acceleration in the vertical direction, since the cord is the only force acting in the horizontal direction. The acceleration can also be calculated using the equation F=ma, where F is the net force and m is the mass of the blocks.