The figure shows two unstretched springs, connected in series to a wall and atta

Question

The figure shows two unstretched springs, connected in series to a wall and attached to a box that can slide on a frictionless surface. The spring constants of the two springs are k1 = 12.6 N/m and k2 = 44.3 N/m. A force is applied to the block that moves it to the right and brings it to rest a distance of 15.8 cm to the right of its initial position. Calculate the magnitude of this force. Hint: There is zero net force on the point where the two springs meet. This implies a relationship between the amounts the two springs stretch.

Please explain the work, I want to understand how to approach this. Thanks in advance :)

Explanation / Answer

Here ,

k1 = 44.3 N/m

k2 = 12.6 N/m

for the springs in series ,

1/Keq = 1/44.3 + 1/12.6

Keq = 9.81 N/m

let the force is F

for the equilibrium

F = Keq * x

F = 9.81 * 0.158

F = 1.55 N

the applied force is 1.55 N

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