Accelerations of Two Blocks Connected by a String

In summary, two blocks of equal mass are connected by a string and have different spring constants (k1 > k2). When the left block is pulled down and released, the acceleration of each block can be found by combining the forces acting on each block and applying Newton's 2nd law.
  • #1
lektor
56
0
two blocks of equal mass are connected by an ideal string.
the values of m, k1 and k2 are given (k1 > k2 ). Initially, both springs are relaxed. Then the left block is slowly pulled down a distance x and released.
Find the acceleration of each block.


sorry about no latex in a hurry :)

F = ma
F = -Kx

ma = -kx

a = -kx/m

Since extension is occurring on the left hand side x is positive.
Since compression takes place on the right hand side x is negitive.

a = -k(+or-x)/m


I was in a bit of a hurry but I've tested with some values and it seems ok, but i'd love some help if this is wrong.
 
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  • #2
Springs or strings or both or none?

I'm sorry, you haven't been able to pose your problem clearly here.
Try again..
 
  • #3
let me get the diagram it is rather tricky
 

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  • #4
I suggest you start by indentifying all the forces acting on each mass, then write Newton's 2nd law for each separately. Combine those two equations and solve for the acceleration. (Don't forget that they are attached by a string.)
 

1. What is spring acceleration?

Spring acceleration refers to the rate at which an object attached to a spring increases in speed due to the restoring force of the spring.

2. What factors affect spring acceleration?

The factors that affect spring acceleration include the mass of the object attached to the spring, the spring constant, and the distance the spring is compressed or stretched.

3. How is spring acceleration calculated?

Spring acceleration can be calculated using the formula a = F/m, where a is acceleration, F is the force exerted by the spring, and m is the mass of the object.

4. Can spring acceleration be negative?

Yes, spring acceleration can be negative if the restoring force of the spring is acting in the opposite direction of the motion of the object attached to it. This can happen, for example, if the spring is compressed and then released, causing the object to move in the opposite direction of the compression.

5. How does spring acceleration relate to Hooke's law?

Hooke's law states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. This means that as the spring is compressed or stretched, the force exerted by the spring increases, resulting in a greater acceleration of the attached object.

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