The work done in stretching or compressing a spring is
proportional to the square of the displacement
. If we double the displacement, we do 4 times as much work. It takes 16 J to stretch the spring 20 cm from its unstretched length, so it takes 12 J to stretch it from 10 cm to 20 cm.
What is the work done in stretching the spring?
the gradient is the spring constant.
the area under the line
is the work done in stretching the spring.
How much work is done in stretching a spring of spring constant k from its unstretched?
Question: When a spring with spring constant k is stretched by distance L from its unstretched length L0 by an external force acting parallel to the string (figure a), the work done by the external force is
W=(1/2)kL2
. This work equals the potential energy of the stretched spring.
How do you calculate work done by a spring?
Also, we can see that in a cyclic process, the work done by the
springs force is zero
. Hence, we can say that the spring force is a conservative force because it depends on the initial and final positions only. Therefore, this work done is in the form of the Spring potential energy.
How do you calculate the work done in extending a spring?
Let the spring be stretched through a small distance d x dx dx. Then work done in stretching the spring through a distance d x dx dx is
d W = F d x
, dW=Fdx, dW=Fdx, where F is the force applied to stretch the spring.
How far will a spring stretch equation?
F = -kx
. The proportional constant k is called the spring constant. It is a measure of the spring's stiffness. When a spring is stretched or compressed, so that its length changes by an amount x from its equilibrium length, then it exerts a force F = -kx in a direction towards its equilibrium position.
Is spring force constant?
The force exerted by a spring on objects attached to its ends is proportional to the spring's change in length away from its equilibrium length and is always directed towards its equilibrium position. … The
proportional constant k
is called the spring constant.
Can work done by a spring be positive?
You pull a spring to extend it. The force you exert on the spring is in the same direction as your displacement. You have
done positive
work on the spring. The force that the spring exerts on you is in the opposite direction to its displacement so the spring has done negative work.
What is work done formula?
Work, in physics, measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement. … If the force is being exerted at an angle θ to the displacement, the work done is
W = fd cos θ.
Can work done by spring be negative?
The minus sign indicates that the spring force is always opposite in direction to the displacement of its free end. So the work done by a
spring force is always negative
.
What force is needed to extend a spring?
The proportional constant k is called the spring constant. It is a measure of the spring's stiffness. When a spring is stretched or compressed, so that its length changes by an amount x from its equilibrium length, then it exerts a
force F = -kx in
a direction towards its equilibrium position.
What is the equation for energy stored in a spring?
| Equation Symbols Meaning in words | U s = 1 2 k x 2 U_s = dfrac{1}{2}k x ^2 Us=21kx2 U s U_s UsU , start subscript, s, end subscript is the elastic potential energy Elastic potential energy is directly proportional to the square of the change in length and the spring constant. |
|---|
Does the spring constant depend on how far the spring is stretched?
More generally, the spring constant of a
spring is inversely proportional to the length of the spring
, assuming we are talking about a spring of a particular material and thickness. … That is because the spring constant and the length of the spring are inversely proportional.
What is a normal spring constant?
The normal spring constant value is
a measure of how much force has to be applied to cause a deflection of unit length at the free end of the cantilever
.
How do you find the maximum compression of a spring?
⇒F=kx , here F is the force applied by a spring having the spring constant k due to an extension x in the spring. Thus the maximum compression of the spring comes out to be equal to
mak
.
