Soru
CHECKPOINT 1. What is the spring constant for a spring that starts at a length of 25 cm and extends to a length of 32 cm when a mass of 50g is added?
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4.2
(251 Oylar)
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Profesyonel · 6 yıl öğretmeni
Uzman doğrulaması
Cevap
To find the spring constant (k) for a spring, we can use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement of the spring from its equilibrium position. The formula for Hooke's Law is:F = kxwhere F is the force applied to the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position.In this case, we are given the initial length of the spring (25 cm) and the final length of the spring (32 cm) when a mass of 50g is added. We can calculate the displacement (x) by subtracting the initial length from the final length:x = 32 cm - 25 cm = 7 cmNext, we need to calculate the force (F) exerted by the mass. The force exerted by a mass is given by the formula:F = mgwhere m is the mass and g is the acceleration due to gravity. In this case, the mass is 50g, which is equal to 0.05 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. Plugging in these values, we get:F = (0.05 kg)(9.8 m/s^2) = 0.49 NNow that we have the force and the displacement, we can plug these values into Hooke's Law to solve for the spring constant:0.49 N = k(0.07 m)Dividing both sides of the equation by 0.07 m, we get:k = 0.49 N / 0.07 m = 7 N/mTherefore, the spring constant for the spring in this case is 7 N/m.