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The restoring force of a spring is proportional to the displacement of the object at the end?
Wiki User
∙ 9y ago
The formula called Hooke's first law says that:
"F"(being the restoring force) = "-k"(the spring constant) times "x" (the displacement)
the negative is only for notations sake. and yes this means they are proportional, by means of the constant.
Wiki User
∙ 9y ago
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How does the elastic potential energy in a mass spring system change if the displacement of the mass is doubled?
The elastic potential energy (EEp) of the spring with displacement x from its original length is given by: EEp = 1/2 kx2 (can be proved using integration) where k is the spring constant of the spring. So, if the displacement of the mass is doubled, the elastic EEp stored will increase by 22, that is by 4.
Is the period of a vibrating spring linearly affected by the mass of the attached object?
Let a mass m be attached to the end of a spring with spring constant k. The spring extends and comes to rest with an equilibrium extension e. At equilibrium; Weight = Force exerted by spring => mg = ke -------- 1 Suppose the spring is displaced through a displacement x downwards from its equilibrium position: Resolving vertically, we have; Resultant force on mass = Force exerted by spring - Weight of mass => ma = k(e + x) - mg ------- 2 From 1, we have: ma = mg + kx - mg => a = (k/m)x Since a is proportional to displacement from equilibrium position, the oscillation is simple harmonic. So, (angular velocity)2 = (k/m) => 2pi/T = (k/m)1/2 => T = 2pi (m/k)1/2 This equation shows that the time period is proportional to the square root of the mass of the attached object.
How does a spring scale operate?
A spring scale is simply a spring fixed at one end with a hook to attach an object at the other. It works on the principle of Hookes Law, that states that the force needed to extend the spring is proportional to the distance that the spring extended from it's fixed position.
What forces causes the spring to be stretched?
External force or you can say deformation force causes spring to stretch and restoring force is developed due to introduction of restoring strain in spring to restore in its original shape.
What happens to a springs force if you stretch it more?
It may loose its elastic nature.
Want is the aim of hookes law?
Hooke's law was designed to determine the restoring force of a spring, given its spring constant and the displacement of the spring from its equilibrium position. The law is written as follows: F = -kx; in which "F" is the restoring force, "k" is the spring constant, and "x" is the spring's displacement.
Difference between Harmonic oscillator and anharmonic oscillator?
In case of HARMONIC OSCILLATOR the relation b/n FORCE AND DISPLACEMENT is LINEAR but in the case of ANHARMONIC OSCILLATOR relation b/n force and displacement is not linear.Hence this non-linearity arises the fact that the spring is not capable of exerting a restoring force that is proportional to the displacement.
What property of a spring makes it suitable to measure a force?
The fact that the displacement of the spring (the amount it stretches) is proportional to the force.
When a spring under stretch or compressionthe magnitude of the restoring force that restores into equilibrium position according to hooks law is proportional to?
The original length of the spring and the modulus of elasticity.
What does the spring constant k mean?
The spring constant is a measure of stiffness - the ability to resist displacement under a load. It is denoted by K where F = kx where f = load force and x = displacement
What is the mathematical relationship between force and displacement?
For a simple harmonic oscillator, the force is proportional to the displacement F=-kx, where F is the force, x is the displacement, and k is a positive proportionality constant commonly referred to as the spring constant
How does the elastic potential energy in a mass spring system change if the displacement of the mass is doubled?
The elastic potential energy (EEp) of the spring with displacement x from its original length is given by: EEp = 1/2 kx2 (can be proved using integration) where k is the spring constant of the spring. So, if the displacement of the mass is doubled, the elastic EEp stored will increase by 22, that is by 4.
What is the work of galvanometer?
Moving coil galvanometer? If so, it is effectively an electric motor acting against a spring. the force from the motor is proportional to the current and the force from the spring is proportional to displacement. When they are equal, the needle (attached to the motor), stops. Moving iron meters rely on opposite magnetic poles repelling.
Is the period of a vibrating spring linearly affected by the mass of the attached object?
Let a mass m be attached to the end of a spring with spring constant k. The spring extends and comes to rest with an equilibrium extension e. At equilibrium; Weight = Force exerted by spring => mg = ke -------- 1 Suppose the spring is displaced through a displacement x downwards from its equilibrium position: Resolving vertically, we have; Resultant force on mass = Force exerted by spring - Weight of mass => ma = k(e + x) - mg ------- 2 From 1, we have: ma = mg + kx - mg => a = (k/m)x Since a is proportional to displacement from equilibrium position, the oscillation is simple harmonic. So, (angular velocity)2 = (k/m) => 2pi/T = (k/m)1/2 => T = 2pi (m/k)1/2 This equation shows that the time period is proportional to the square root of the mass of the attached object.
How does a spring scale operate?
A spring scale is simply a spring fixed at one end with a hook to attach an object at the other. It works on the principle of Hookes Law, that states that the force needed to extend the spring is proportional to the distance that the spring extended from it's fixed position.
What forces causes the spring to be stretched?
External force or you can say deformation force causes spring to stretch and restoring force is developed due to introduction of restoring strain in spring to restore in its original shape.
What happens to a springs force if you stretch it more?
It may loose its elastic nature.
