Question

When a spring is stretched from its relaxed position, the force exerted by the spring is equal to 2.035 times the length. Let's say we use a mechanical device to pull the spring. The force exerted by the device is equal to the root of 3 more than 12 times the distance the device has pulled the spring. The length is measured in inches, and the force exerted by the device is measured in pounds/inch. How can you determine the point at which the device will no longer be able to pull the spring?

A) By setting up a quadratic equation representing the force exerted by the spring and the force exerted by the device, then solving for the distance when the two forces are equal.

B) By graphing the forces as functions of distance and finding the point of intersection.

C) By calculating the equilibrium point where the force exerted by the spring matches the force exerted by the device.

D) By using calculus to find the critical points of the function representing the forces and determining where they are equal.

Answer 1

The point at which the device will no longer be able to pull the spring can be determined by setting up a quadratic equation and solving for the distance when the forces are equal.

Step-by-step explanation:

The point at which the device will no longer be able to pull the spring can be determined by setting up a quadratic equation representing the force exerted by the spring and the force exerted by the device, and then solving for the distance when the two forces are equal. This can be done by equating the force exerted by the spring (2.035 times the length) to the force exerted by the device (square root of 3 more than 12 times the distance). By finding the distance at which these forces are equal, you can determine the point at which the device will no longer be able to pull the spring.