Question

The average value of the load between A and B is 6.0 N. The spring has an unstretched lengthincreases from 4.0 cm to 6.0 cm.

Answer 1

To find the force constant of the spring and its unloaded length, we can use Hooke's law and the given masses and lengths of the spring. By setting up equations and solving for the force constants, we can determine the force constant for each mass. The unloaded length of the spring can be found by subtracting the displacement caused by the mass from its stretched length.

Step-by-step explanation:

To find the force constant of the spring, we can use Hooke's law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. For the given problem, we have two different masses and lengths of the spring. By applying Hooke's law, we can set up two equations and solve for the force constants. The unloaded length of the spring can be found by subtracting the displacement caused by the mass from its stretched length.

1. (a) The force constant of the spring can be found by dividing the weight of the mass by its displacement. For mass 1 with a weight of 0.3 kg and a displacement of 0.55 m, the force constant is (0.3 kg x 9.8 m/s^2) / 0.55 m = 5.45 N/m. For mass 2 with a weight of 1.95 kg and a displacement of 0.55 m, the force constant is (1.95 kg x 9.8 m/s^2) / 0.55 m = 34.91 N/m.
2. (b) The unloaded length of the spring can be found by subtracting the displacement caused by the mass from its stretched length. For mass 1, the unloaded length is 0.55 m - 0.2 m = 0.35 m. For mass 2, the unloaded length is 0.55 m - 0.75 m = -0.2 m. This negative value suggests that the spring is compressed when it is unloaded.