# WORK AND ENERGY

• WORK, in the physics sense, is the product of the component of the force along the line of motion and the distance the object moves along that line.

W = (Fcosq )s

• Work is a scalar that can be written as the dot (or scalar) product of the force and the displacement.

Work = F· s

• Work can be positive or negative
• The units for work include joules (newton-meter) and the ft-lb.
• If the force changes and is a function of position, then we have to use integration to determine the work done as the object moves between two locations.

• The force exerted by a spring (F = -kx) depends on the amount of spring extension or compression.

• For one-dimensional motion, an unbalanced force can produce an acceleration which causes the velocity to change. The work done can be related to the change in the "motional energy". This energy of motion is called the kinetic energy: KE = (1/2)mv2.
• Is this concept valid for a force which is not constant but changes with time or position?

• Power is the rate at which work is done: P = (work)/(time) = dW/dt

EXAMPLES

• If an object is dropped from a height h, what is the kinetic energy just before it hits the ground?

• An object is dropped from an airplane flying horizontally at 30 m/s. If the height is 80 m, what is the speed of the object just before it hits the ground? Let g = 10 m/s2.

• A car uses 100 hp and moves at 60 mph. What is the forward thrust of the engine?