Unit 3: Work, Energy, and Power

18 terms. Say what each one means, then open the card to check.

• Kinetic energy

  The energy of motion, $K = \tfrac{1}{2}mv^2$, in joules. It is never negative and grows with the square of the speed.

  Example. A 4.0 kg cart moving at 2.0 m/s has 8.0 J of kinetic energy; at 4.0 m/s it has 32 J.

• Work

  The energy a force transfers into or out of a system as the object moves: $W = Fd\cos\theta$ for a constant force, where θ is the angle between the force and the displacement.

  Example. Pushing a stalled car 5.0 m with a steady 300 N forward force does 1,500 J of work on it.

• Joule

  The unit of energy and of work, equal to a force of one newton acting through one meter (1 J = 1 N·m).

  Example. Lifting a 100 g apple straight up by 1 m takes about 1 J of work.

• Positive and negative work

  A force does positive work when it has a component along the displacement, negative work when its component opposes the displacement, and zero work when it is perpendicular to it.

  Example. When you lower a box slowly to the floor, gravity does positive work on the box and your hands do negative work.

• Net work

  The sum of the work done by all the forces on an object, which equals the work done by the net force.

  Example. If a rope does 50 J of work on a sled and friction does -20 J, the net work on the sled is 30 J.

• Work-energy theorem

  Add up the work done by every force on an object and you get exactly how much its kinetic energy changes: $W_{\text{net}} = \Delta K$.

  Example. A 3.0 kg puck at rest that receives 24 J of net work ends up with 24 J of kinetic energy, moving at 4.0 m/s.

• Area under a force-position graph

  The work done by that force over the displacement; area below the position axis counts as negative work.

  Example. A force that holds steady at 5 N over 4 m does 20 J of work, the area of a 5-by-4 rectangle.

• Gravitational potential energy

  Energy stored in an object-Earth system because of their separation. Near Earth’s surface its change is $\Delta U_g = mg\Delta y$.

  Example. Raising a 1.0 kg bag of flour 2.0 m onto a high shelf increases the bag-Earth system’s potential energy by about 20 J.

• Elastic potential energy

  Energy stored in a stretched or compressed spring, $U_s = \tfrac{1}{2}kx^2$, so doubling the stretch stores four times the energy.

  Example. A spring with k = 600 N/m compressed 0.20 m stores 12 J.

• Zero of potential energy

  The position where you choose U = 0. The choice is free, because only changes in potential energy affect the motion.

  Example. Measuring heights from the floor or from the tabletop gives a book different values of $U_g$ but the same change when it falls.

• Conservative force

  A force, such as gravity or a spring force, whose work depends only on the starting and ending positions, so its effect can be stored as potential energy.

  Example. Gravity does the same work on a crate whether it is lifted straight up 2 m or pushed up a frictionless ramp to the same height.

• Mechanical energy

  The sum of the kinetic and potential energies of a system, $E = K + U$.

  Example. A swinging pendulum trades kinetic and potential energy back and forth while their sum stays nearly constant.

• Conservation of energy

  The total energy of a system changes only by energy transferred across its boundary, such as work by outside forces; inside the system, energy only changes form.

  Example. In a sealed, insulated flask, a reaction can turn stored chemical energy into thermal energy, but the flask’s total energy stays the same.

• Closed system

  A system with no work done on it by outside forces and no other energy crossing its boundary, so its total energy stays constant.

  Example. A falling ball and Earth together form a system whose mechanical energy stays constant while the ball falls, if air resistance is ignored.

• Thermal energy from friction

  Kinetic friction between sliding surfaces turns mechanical energy into thermal energy; for an object sliding a distance d, the increase is $f_kd$.

  Example. Rubbing your palms together for a few seconds warms them: the work you do against friction becomes thermal energy.

• Energy bar chart

  A diagram with a bar for each kind of energy at two moments, plus a bar for energy transferred in or out, that shows how energy is shared and conserved.

  Example. For a ball dropped from rest, the chart starts with all gravitational energy and ends with all kinetic energy just before impact.

• Power

  The rate at which energy is transferred or work is done, $P = \Delta E/\Delta t$, measured in watts (1 W = 1 J/s).

  Example. A motor that does 600 J of work in 3.0 s delivers an average power of 200 W.

• Instantaneous power

  The power a force delivers at one instant; for a force acting along an object’s motion, $P = Fv$.

  Example. A rope pulling a sled forward with 50 N at a steady 2.0 m/s delivers 100 W.