Work and Energy

Work in physics has a specific meaning - it occurs when a force causes an object to move. The formula W=Fd·cosθ calculates work, measured in Joules, where F is force, d is displacement, and θ is the angle between them. The angle determines whether work is positive, negative, or zero.

When force and displacement point in the same direction $θ=0°$, work is positive. For instance, pushing a book upward with your hand does positive work. When they point in opposite directions $θ=180°$, work is negative, like when a book moves downward against your push. When force and displacement are perpendicular $θ=90°$, no work is done.

Kinetic energy represents the energy an object has due to its motion, calculated as KE=½mv². Unlike work, kinetic energy is always positive and is measured in joules. The formula shows that doubling an object's speed quadruples its kinetic energy!

💡 When solving work problems, you typically don't need to break forces into components because the angle θ is already included in the work equation.

Some forces like gravity and normal force often do zero work in certain scenarios. For example, when an object moves horizontally, gravity acts perpendicular to the motion, resulting in zero work from gravity.