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A 31.0 cm long spring is hung vertically from a ceiling and stretches to 39.3 cm when a 7.00 kg mass is hung from its free end.

(a) Find the spring constant (in N/m).

(b) Find the length of the spring (in cm) if the 7.00 kg weight is replaced with a 185 N weight.

Answer :

Final answer:

To answer this question, we apply Hooke's Law and the formula for gravitational force to calculate the spring constant with a 7.00 kg mass, and then use that constant to find the spring length with a 185 N weight.

Explanation:

The towing force from a spring, known as Hooke's Law, is given by F=-kx, where F is the force, k is the spring constant, and x is the displacement from the spring's equilibrium position. Here, the 7.00 kg mass generates a force due to gravity, F=mg, where m is the mass and g is gravitational acceleration (approximately 9.80 m/s²). We can find the spring constant (k) by rearranging the equation, k=-F/x.

(a) To find k when a 7.00 kg mass is hung from the spring, we find the displacement (the stretched length of 39.3 cm minus the spring's original length of 31.0 cm) and apply Hooke's Law.

(b) To find the length of the spring when a 185 N weight replaces the 7.00 kg weight, we need to use the spring constant from part (a). The force for this weight is already given, so we rearrange the formula to solve for displacement x=F/k, and add it to the unstretched spring length to find the total length.

Learn more about Hooke's Law here:

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