Work, Energy, and Power

the work done on a body by a single external force F is defined by the equation

dW = F * dr

If n external forces are acting on an object simultaneously, the net work is

dW = F_net * dr

The net work is equal to the algebraic sum of

the work done by each individual force. (A * B + C * B = (A+C) * B

Another equation for work due to multiple forces

TO calculate the net work done by multiple forces, you have two options

1. calculate the work done by each force and sum these individual works

2. calculate the net force and compute the work done by the net force using the equation dW = F_net * dr

Work and energy have units of

newton * meter, or a joule

kg*m²/s²B

Work is a scalar whose magnitude and sign

are determined by the component of the net force parallel to the direction of motion

the displacement vector dr is parallel to the

velocity

work is negative when

the force has a component antiparallel to the displacement vector dr and thus antiparallel to the velocity.

• tangential acceleration causes the object’s speed to decrease

When work is zero,

the force has no c opponent parallel or the displacement vector dr

• no component parallel to the velocity

• no tangential acceleration

• speed does not change

When work is positive,

The force has a component parallel to the displacement vector dr and the velocity

• tangential acceleration parallel to velocity

• increases object’s speed

For constant forces, we can evaluate the work integral

W = F * Δr

work due to a constant net force

For 1D motion, work equals

W = ∫ F_x dx

• work = area underneath F_x(x) curve

kinetic energy equation

KE = mv²/2

• similar to work and other forms of energy, KE has units of joules