Work done by variable force Spring force

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Work done by variable force requires integration of work done by the variable force at each step. Spring force is a good example of variable force and work done by this variable force is what we will study here. • Solved numerical problems and downloadable PDFs: ▶ https://thesciencecube.com/ • Join our Telegram Channel: ▶ https://t.me/TheScienceCube_Community • The variable spring force acts opposite the direction of displacement and reduces the kinetic energy as it increases in magnitude. • Key Moments: • 00:00 Work done by variable force (introduction) • 00:25 Spring mass setup and force due to the spring • 00:43 What is a restorative force • 01:05 Spring force acts opposite the displacement • 01:20 Spring force F = -kx • 01:48 What does negative sign indicate in F = -kx • 02:20 Reduction in kinetic energy as the spring is pulled • 04:30 Derivation of the equation F = -kx • So in this lesson we will deal with forces that are variable in nature and how we can find work done by this variable force when it displaces a mass. To understand this we will take a box and attach it to a spring with the other end of the spring attached to rigid wall. Now if you pull the box to the right, or give it displacement in the right direction, the spring will elongate and what you will intuitively know is that the spring would tend to pull it back into its normal rest position with a certain force. This force is also often called the restorative force because it is trying to restore its normal position. As you pull the mass further to the right, the spring elongates further and this restorative force increases further. So what you see is that the spring force that is pulling back the mass in a direction opposite to the displacement is changing or is variable. So this force is given by the formula F= -kx where k is the spring constant or a measure of stiffness of the spring. Larger the value of the constant, more the force with which it will pull back the mass. The negative sign indicates that the force acts in a direction opposite to the displacement. So when you move mass to the right the spring will pull the mass to the left. Likewise if you push the box to the left and compress the spring, the spring will push the mass to the right.

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