# 13.6 Work by spring force

 Page 1 / 2
Nature of spring force is to restore its configuration.

Spring is an arrangement, which is capable to apply force on a body. As we will see, spring force is similar to gravity in many important ways. At the same time, it is different to gravity in one important way that it applies a variable force unlike gravity.

In this module, we shall first outline the characterizing aspects of spring and then develop an expression for work. Subsequently, we shall analyze situations first with spring force alone and then along with other external force(s) on similar line as in the case of work by gravity.

## Spring force

Spring force is given by the expression :

$\begin{array}{l}F=-kx\end{array}$

where k is spring constant, measured experimentally for a particular spring. The value of k (=-F/x) measures the stiffness of the spring. A high value indicates that we would require to apply greater force to change length of the spring.

This relationship, defining spring force, is also known as “Hooke’s law”, which is valid under two specific conditions :

• The mass of spring is negligible (and can be neglected).
• There is no dissipative force (like friction) involved with spring.

The attribute “x” is measured from the position of “neutral length” or “relaxed length” - the length of spring corresponding to situation when spring is neither stretched nor compressed. We shall identify this position as origin of coordinate reference.

The negative sign in the expression indicates an important aspect of the nature of spring force that it is always opposite to the direction of the displacement. It means that it is always directed towards the position at neutral length i.e. origin. See the figure to visualize how spring force is always directed towards origin.

## Context of spring force

The forces on the body (block) attached to a horizontal spring may include friction, if the surfaces between block and the surface is rough. For the sake of simplicity, however, we shall consider the surface to be smooth. The force due to gravity and normal force are normal to the motion and do not influence force analysis here. As such, we will not consider either friction or gravity, while calculating work for the motion on smooth horizontal surface.

Just like the case of gravity, there are two situations with respect to application of force on a body by the spring.

1: In one case, the body is given a jerk, say towards right and the body is let go. In this case, the only force on the block is spring force. This situation is similar to vertical projection of an object with an initial speed. This case of spring force, therefore, is specified by an initial speed, preferably at the origin as shown in the figure.

2: In other case, there is external force(s) in addition to spring force. The horizontal force is continuously applied on the block as it moves along the surface. This situation is similar to the case of pulling a lift vertically by string and pulley arrangement. In this case, we may be required to analyze external force with the help of “free body diagram”.

#### Questions & Answers

water boil at 100 and why
what is upper limit of speed
what temperature is 0 k
Riya
0k is the lower limit of the themordynamic scale which is equalt to -273 In celcius scale
Mustapha
How MKS system is the subset of SI system?
which colour has the shortest wavelength in the white light spectrum
how do we add
if x=a-b, a=5.8cm b=3.22 cm find percentage error in x
x=5.8-3.22 x=2.58
what is the definition of resolution of forces
what is energy?
Ability of doing work is called energy energy neither be create nor destryoed but change in one form to an other form
Abdul
motion
Mustapha
highlights of atomic physics
Benjamin
can anyone tell who founded equations of motion !?
n=a+b/T² find the linear express
أوك
عباس
Quiklyyy
Moment of inertia of a bar in terms of perpendicular axis theorem
How should i know when to add/subtract the velocities and when to use the Pythagoras theorem?
Centre of mass of two uniform rods of same length but made of different materials and kept at L-shape meeting point is origin of coordinate
A balloon is released from the ground which rises vertically up with acceleration 1.4m/sec^2.a ball is released from the balloon 20 second after the balloon has left the ground. The maximum height reached by the ball from the ground is