When a vertically oriented spring scale supports a 180180 N block, the spring stretches 0.30.3 m from rest. Neglecting any other masses associated with the scale, what is the value of the spring constant?1. 3030 N/m2. 294294 N/m3. 600600 N/m4. 58805880 N/m
Question
When a vertically oriented spring scale supports a 180180 N block, the spring stretches 0.30.3 m from rest. Neglecting any other masses associated with the scale, what is the value of the spring constant?1. 3030 N/m2. 294294 N/m3. 600600 N/m4. 58805880 N/m
Solution
To find the value of the spring constant, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
Hooke's Law can be written as F = kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement of the spring.
In this case, the force exerted by the spring is equal to the weight of the block, which is 180 N. The displacement of the spring is given as 0.30 m.
Plugging these values into Hooke's Law, we have 180 N = k * 0.30 m.
To solve for k, we can rearrange the equation to k = 180 N / 0.30 m.
Evaluating this expression, we find that k = 600 N/m.
Therefore, the value of the spring constant is 600 N/m.
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