We have learned that materials stretched within their exhibit linear – behavior. Springs allow us to adjust the amount of strain that occurs for a given stress and increase the size of the linear region. For example, take a steel rod one foot in length and the diameter of a clothing thread and you would not be able to noticeably stretch that rod with your bare hands. However, if that rod were formed into a spring, then you could stretch the spring with your bare hands.
Springs follow which states that the restoring force, FR exerted by the spring is equal to the stretch or compression distance, known as the (Δx), multiplied by spring stiffness (k) and the direction of the force is opposite to the direction of the displacement.
A higher spring stiffness means the spring shows a greater resistance to stretching or compressing. Spring stiffness is often called the .
Check out this simulation of :
If the spring scale shown in the previous image reads 6 N when is 3 cm, what is the (stiffness) in units of N/cm?
The standard unit for spring constant is N/m. Convert your answer from N/cm to N/m.
Weight with a Spring Scale
Spring scales are designed to take advantage of to determine the size of the stretching the spring by measuring the . In order to use a spring scale to measure we can multiply the measured stretch distance by the known to find the applied by the spring. Typically spring scales will have markings on them which indicate the restoring force for each stretch distance, so we don’t have to actually calculate the restoring force every time we use the scale. If the object being weighed is in then the restoring force and the weight of the object are the same, and so by measuring the restoring force with the scale we then know the weight. For example when hanging the object from the spring scale the will pull it down and the in the spring pulls it up, as in the image below. If instead the scale is tilted so gravity and restoring force don’t have opposite directions, the reading may be inaccurate. If the object and/or scale are not in while holding it, then the reading may be inaccurate, and we will learn more about how and why in later units. Either way, the scale is only accurate if the object being weighed remains in equilibrium during the measurement.
Many analog scales are based on multiple springs or the resistance to deformation by objects other than springs, but they still determine weight using measurement of a deformation combined with a known relation between deformation and force.
Many modern scales follow the same principle as spring scales, but instead of measuring the deformation directly, they measure an electric voltage created by a material in response to being deformed. Materials that produce voltages in response to deformation are known as . As long as the relations between voltage and deformation and between deformation and applied force are both known, the scale can determine your weight by measuring a voltage.
An interesting aspect of the piezoelectric effect is reversibility, meaning that piezoelectric materials not only produce a voltage in response to deformation, they will also deform in response to an applied voltage, which allows for piezoelectric motors.
- OpenStax University Physics, University Physics Volume 1. OpenStax CNX. Sep 14, 2018 http://firstname.lastname@example.org. ↵
- "Paula Khan" by Neal Snyder via Wikimedia Commons released in the public domain by U.S. Army Environmental Command ↵
region of the stress vs. strain curve for which stress is proportional to strain and the material follows Hooke's Law
a physical quantity that expresses the internal forces that neighboring particles of material exert on each other
the measure of the relative deformation of the material
the restoring force exerted by a spring is equal to the displacement multiplied by spring constant
change in position, typically in reference to a change away from an equilibrium position or a change occurring over a specified time interval
measure of the stiffness of a spring, defined as the slope of the force vs. displacement curve for a spring
any interaction that causes objects with mass to change speed and/or direction of motion, except when balanced by other forces. We experience forces as pushes and pulls.
the force of gravity on on object, typically in reference to the force of gravity caused by Earth or another celestial body
a force that tends to move a system back toward the equilibrium position
a state of having no unbalanced forces or torques
attraction between two objects due to their mass as described by Newton's Universal Law of Gravitation
the ability of certain materials to generate an electric charge in response to applied mechanical stress