Work and Energy
Mechanical work, work-energy theorem, kinetic energy, potential energy, and dissipation.
General idea of the topic
Work and energy offer an alternative way of solving mechanics problems: instead of following the motion instant by instant, the initial and final states are compared. Work measures the transfer of energy by a force, and energy is the capacity of a system to do work.
The block covers the forms of mechanical energy and their balance: work and power, kinetic energy, gravitational and elastic potential energy, conservation in conservative systems, the effect of non-conservative forces and rotational energy.
What you will truly understand
By the end you will be able to compute the work of constant and variable forces, apply the work-kinetic energy theorem, use conservation of mechanical energy and account for the energy dissipated by friction.
You will also be able to choose between a force approach and an energy approach according to what is asked.
Recommended learning route
- Fundamentals: work of a force, variable forces and power.
- Kinetic Energy: kinetic energy and the work-energy theorem.
- Potential Energy: gravitational and elastic potential energy, and their relation to force.
- Conservation of Energy: conservation of mechanical energy in conservative systems.
- Non-Conservative Forces: friction, dissipation and work of non-conservative forces.
- Rotational Energy: rotational kinetic energy and its role in the balance.
Physical criterion you must acquire
The essential criterion is that energy is used when the initial and final states matter and not the time or the detailed path. If there are non-conservative forces, W_nc = ΔE_mech is written; if not, E_mech is conserved. A negative kinetic energy result indicates an error in the setup.
Connection with real problems
- roller coasters and pendulums.
- vehicles, braking and consumption.
- machines and efficiency.
- power plants.
Final goal of the topic
The final goal is to set up the energy balance of any mechanical system, identify which forces do work and obtain speeds, heights or dissipated energy rigorously.
Topics in this section
- Fundamentals (Work and Energy)
Scalar definition of work as a line integral of force along a displacement path.
- Kinetic Energy
Energy associated with motion and with the net work that changes speed.
- Potential Energy
Conservative force fields, gravitational, and elastic potential energy functions.
- Conservation of Energy
Universal principle of mechanical energy conservation in closed and isolated systems.
- Non-Conservative Forces
Energy balance with dissipative non-conservative forces and thermal energy degradation.
- Rotational Energy
Evaluating rotational kinetic energy and work done by torques on rotating bodies.