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Chapter 1: Problem 87

The force \(F\) a spring exerts on you is directly proportional to the distance \(x\) you stretch it beyond its resting length. Suppose that when you stretch a spring \(8.00 \mathrm{~cm},\) it exerts a 200. N force on you. How much force will it exert on you if you stretch it \(40.0 \mathrm{~cm} ?\)

Short Answer

Expert verified
Answer: The force exerted on the user if the spring is stretched to 40 cm is 1000 N.

Step by step solution

01

Setup the equation

The given equation is \(F = kx\). Given that \(F=200\) N and \(x=0.08\) m, we can setup the equation as: \(200 = k \times 0.08\).
02

Solve for the proportionality constant (k)

Rearrange the equation to solve for k: \(k = \frac{200}{0.08}\). After calculating, we get \(k = 2500\) N/m.
03

Use the proportionality constant to find the force exerted by the spring when it is stretched to 40 cm

In this step, we will use the constant k to find the force exerted by the spring when it is stretched to 40 cm. We have \(F = kx\). Convert 40 cm to meters (1 cm = 0.01 m): \(x = 0.4\) m. Then plug in the values: \(F = 2500 \times 0.4\).
04

Calculate the force

After calculating, we get the force as: \(F = 2500 \times 0.4 = 1000\) N. Final Answer: The force exerted on the user if the spring is stretched to 40 cm is 1000 N.

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