# 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.