Video: US-SAT05S4-Q16-130121496964

The amount of force it takes to compress a spring can be approximated using the formula 𝐹 = π‘˜π‘₯, where 𝐹 is the force in newtons, π‘˜ is the spring constant in newtons per millimeter, and π‘₯ is the displacement (or change in the length of the spring) in millimeters. The given table shows the spring constants for 7 different types of springs. What is the force, in newtons, that would develop in a type C spring if it was subjected to a compression of 5 mm?

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Video Transcript

The amount of force it takes to compress a spring can be approximated using the formula 𝐹 equals π‘˜π‘₯, where 𝐹 is the force in newtons, π‘˜ is the spring constant in newtons per millimeter, and π‘₯ is the displacement or change in the length of the spring in millimeters. The given table shows the spring constants for seven different types of springs. What is the force in newtons that would develop in a type C spring if it was subjected to a compression of five millimeters?

If we consider our formula 𝐹 equals π‘˜π‘₯, 𝐹 is the force, which is a measurement of newtons. π‘˜ is a constant value, a measure of newtons per millimeter. And π‘₯ is a displacement, which will be measured in millimeters. If we consider a type C spring, it has a constant value of 15 newtons per millimeter. And that means its π‘˜ value is 15. Type C’s spring constant is 15 newtons per millimeter.

If we subjected this type of spring to a compression of five millimeters, that’s the value of π‘₯. The displacement value as a compression is a type of displacement. And so, we need to multiply our constant by five millimeters. The force in newtons, after we take a type C spring and subject it to a compression of five millimeters, will be 15 times five. We have a fraction of 15 newtons over one millimeter. And we’re multiplying that by five millimeters. The millimeters cancel out. And the force will be 15 times five newtons. The force developed in a type C spring subjected to a compression of five millimeters is 75 newtons.

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