# Force and Potential Energy

**Force and Potential Energy**

**Fundamentals**

- A
**force**is described as a push or pull that has the ability to change an object’s state of motion or its shape. It is measured in Newtons (N). - Forces can be of different types like gravitational force, frictional force, applied force, tension force, and more.

**Potential Energy**

**Potential Energy**is the stored energy in an object due to its position, shape, or state.- It is the energy that has the potential to do work.

**Gravitational Potential Energy**

**Gravitational potential energy**is one form of potential energy, depends on the height of an object and its mass.- This potential energy can be defined mathematically as U = mgh, where U is the potential energy, m is the object’s mass, g is the gravitational constant, and h is the height of the object from the ground.

**Spring Potential Energy**

**Spring potential energy**is another form of potential energy, stored when a spring is stretched or compressed.- This type of energy is given by the formula U = 1/2 kx², with U being the potential energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

**Force and Potential Energy**

- The
**force**exerted by a system undergoing a change in configuration (like a compressed spring or a rock at a height) is related to the gradient of the potential energy with respect to position. - Mathematically, F = -dU/dx, where F is the force, U is the potential energy, and x is the position. The negative sign indicates the force is always directed towards decreasing potential energy.

**Force Partitioning**

- The net force acting on an object can often be
*partitioned*into a part that does work and another part which changes the object’s direction but not its speed. - For instance, in circular motion such as a satellite orbiting Earth, the gravitational force can be divided into a radial part that does no work and a tangential part that does.

Understanding **force**, **potential energy** and their interplay is key for problem-solving in physics. By comprehending their connection, you can gain a deeper understanding of the behaviour of physical systems.