An unstretched spring has a length of 2.0 cm.The spring is then stretched within its limit of proportionality by a tensile force of 1.5 N so that theelastic potential energy stored in the spring is 0.045 J.What is the stretched length of the spring?A 3.0 cm B 5.0 cm C 6.0 cm D 8.0 cm
Question
An unstretched spring has a length of 2.0 cm.The spring is then stretched within its limit of proportionality by a tensile force of 1.5 N so that theelastic potential energy stored in the spring is 0.045 J.What is the stretched length of the spring?A 3.0 cm B 5.0 cm C 6.0 cm D 8.0 cm
Solution
To solve this problem, we need to use the formula for elastic potential energy, which is given by:
E = 1/2 * k * x^2
where E is the elastic potential energy, k is the spring constant, and x is the displacement from the equilibrium position.
We know that E = 0.045 J and the force F = 1.5 N. The force exerted by a spring is also given by F = k * x. We can rearrange this to find k = F / x.
Substituting this into the energy equation gives us:
0.045 = 1/2 * (1.5 / x) * x^2
Solving this equation for x gives us x = 0.03 m or 3 cm. This is the amount the spring is stretched from its equilibrium position.
The unstretched length of the spring is 2 cm, so the total length of the spring when stretched is 2 cm + 3 cm = 5 cm.
So, the answer is B) 5.0 cm.
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