The spring holds the door. In order to open the door by stretching the spring by 3 cm, you need to apply a force equal to 60N. In order to open the door, you need to stretch the spring by 8cm. What work needs to be done to open a closed door?
According to Hooke’s law, the deformation of the spring x is proportional to the applied force F:
x = F / k,
where k is the coefficient of spring stiffness, N / m.
Let us determine the value of k, proceeding from the fact that with a force of F = 60 N, the tension of the spring x = 3 cm = 0.03 m:
k = F / x = 60 / 0.03 = 2000 H / m.
The work required to stretch a spring with a stiffness k by an amount x:
A = k x ^ 2/2.
The required work corresponds to the value x2 = 8 cm = 0.08 m. Substitute the values:
A = 2000 × 0.08 ^ 2/2 = 6.40 J.
Answer: 6.4 J.
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