Chapter 6

• The work done by a constant force is defined as the distance moved multiplied by the component of the force in the direction of displacement.
• In the SI system, the units of work are joules: 1 J = 1 N · m.
• A person does no work on a bag of groceries as long as he does not lift or lower it.
• The force exerted by a person has no component in the direction of motion.
• Power is the rate at which work is done.
• Kinetic energy is the energy of motion, represented by the equation KE = ½ mv^2.
• Potential energy is energy associated with forces that depend on the position or configuration of objects.
• The net work done on an object equals the change in its kinetic energy.
• Work is the product of force and distance, represented by the equation W = Fd cos θ.
• If only conservative forces are acting, mechanical energy is conserved.
• To find the work done by a specific force, draw a free-body diagram, choose a coordinate system, apply Newton’s laws to determine any unknown forces, and find the work done by the force.
• Work done by forces that oppose the direction of motion, such as friction, will be negative.
• For a force that varies, the work can be approximated by dividing the distance up into small pieces, finding the work done during each, and adding them up.
• As the pieces become very narrow, the work done is the area under the force vs distance curve.
• Energy was traditionally defined as the ability to do work.
• Not all forces are able to do work; however, we are dealing in these chapters with mechanical energy, which does follow this definition.
• If we write the acceleration in terms of the velocity and the distance, we find that the work done here is.
• The kinetic energy is defined as:
• An object can have potential energy by virtue of its surroundings, for example, a wound-up spring, a stretched elastic band, an object at some height above the ground.
• Potential energy is a property of a system as a whole, not just of the object (because it depends on external forces).
• Potential energy can be stored in a spring when it is compressed, yielding kinetic energy.
• Potential energy can become kinetic energy if the object is dropped.
• Gravitational potential energy can be defined as the energy stored in an object due to its position in a gravitational field.
• The force required to compress or stretch a spring is k, where k is called the spring constant, and needs to be measured for each spring.
• Kinetic energy is measured in joules.
• If friction is present, the work done depends not only on the starting and ending points, but also on the path taken, making friction a nonconservative force.
• The work done is equal to the change in the kinetic energy: if the net work is positive, the kinetic energy increases; if the net work is negative, the kinetic energy decreases.
• The force increases as the spring is stretched or compressed further.
• The potential energy of the compressed or stretched spring, measured from its equilibrium position, can be written:.
• Potential energy can only be defined for conservative forces.
• The work done by conservative forces is equal to the total change in kinetic and potential energies.
• In raising a mass m to a height h, the work done by the external force is mgh.
• The total mechanical energy is defined as E = KE + PE.
• In the image on the left, the total mechanical energy is: E = KE + PE = ½ mv^2 + mgy.
• The conservation of mechanical energy states that the total mechanical energy is constant.
• If there is no friction, the speed of a roller coaster will depend only on its height compared to its starting height.
• Energy as a whole is conserved.
• The change in gravitational potential energy is the same for walking and running up these stairs, demonstrating that power is needed for acceleration and for moving against the force of gravity.
• The average power can be written in terms of the force and the average velocity: P = Fv.
• For an elastic force, conservation of energy tells us: E = KE + PE = ½ mv^2 + mgy.