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You need to make a spring scale for measuring mass. You want each 1.0 cm length along the scale to correspond to a mass difference of 100 g. What should be the value of the spring constant?

User Dsollen
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1 Answer

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Final answer:

The force constant of a spring can be calculated using Hooke's Law. For this scale, each 1.0 cm length corresponds to a mass difference of 100 g. To find the force constant, we can use the formula k = F / x, where F is the applied force and x is the displacement of the spring. For a 10.0 kg load that stretches the spring by 8.00 cm, the force constant is found to be 1225 N/m.

Step-by-step explanation:

The force constant of a spring is a measure of how stiff or strong the spring is. It is denoted by the symbol k and is determined by Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.

To find the force constant, we can use the formula:

k = F / x

where F is the applied force and x is the displacement of the spring.

In this case, if each 1.0 cm length along the scale corresponds to a mass difference of 100 g, we can use this information to determine the force applied to stretch the spring by 8.00 cm for a 10.0 kg load:

Force = mass * acceleration due to gravity = 10.0 kg * 9.8 m/s^2 = 98 N

Using the formula for force constant, we have:

k = 98 N / 8.00 cm = 1225 N/m

Therefore, the value of the spring constant is 1225 N/m.

User DanyAlejandro
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