Work and Energy Chapter 6

6.1 Work Done by a Constant Force The equation for work tells us the following: In order for work to be done, a force must cause displacement Only the component of force in the direction of motion will cause work to be done. (SOHCAHTOA comes into play here) The derived unit of force is the Newton meter. One Newton meter is referred to as one joule (J).

What the Equation Doesn’t Tell Us Work is a scalar quantity If the displacement is zero, the work done is also zero, even if a force is applied! In the equation, θ is the angle between the force and the displacement. When force points in the same direction as the displacement, θ = 0⁰ and the equation becomes W=Fs

Relating Direction of Force and Displacement The force component perpendicular to the displacement does no work! Work can be (+) or (-), depending on whether a component of the force points in the same direction as the displacement or in the opposite direction. Supersize Who? What is the total work done in completing one “rep” of a bench press?

6.2 The Work-Energy Theorem and Kinetic Energy Newton’s 2nd Law Work Kinematics Work-Energy Theorem F = ma W = Fs Challenge! Use the above equations to come up with an expression relating work (Fs) to kinetic energy (1/2 mv2).

The Solution! The Work-Energy Theorem tells us… Kinetic Energy is… mechanical energy energy of motion like work and all forms of energy, measured in joules The Work-Energy Theorem tells us… When a net external force does work on an object, the KE of the object changes. The difference in KE will equal the work done and vice versa. If work done by the net force is positive, the KE increases. If the word done is negative, the KE decreases. If the work done is zero, the KE remains the same.

6.3 Gravitational Potential Energy We all know that gravity is a force that can cause objects to move toward the Earth or the slow down when moving away from the center of the Earth. In examples where gravity is the force causing work to be done, we use (h) as the symbol for displacement. Yes… h stands for height!

Potential Energy Continued The last given equation is valid for any path taken between initial and final heights (remember displacement!) Vertical distances do not need to be measured with respect to the surface of the earth. PE =mgh Gravitational Potential Energy is.. A “conservative force.” The potential an object has to do work by virtue of the fact that is has moved further from the surface of the earth. Greater as an object moves further from the center of the earth. PE = mgh A scalar quantity

6.4 Conservative vs. Nonconservative Forces The work it does on a moving object is independent of the path between the object’s initial and final position. A force does no net work on an object moving around a closed path when starting position = ending position. Gravitational, elastic spring force, electric force Work done by these forces on objects depends on the path of the motion between the points. Static and kinetic friction, air resistance, tension, normal force, propulsion force of a rocket. Wnc =∆KE + ∆PE This equation applies if gravity is the only conservative force acting on the object.

6.5 Conservation of Mechanical Energy The total mechanical energy acting on a system includes both kinetic and gravitational potential energy. ET = KE + PE When an object is in motion, the total mechanical energy remains constant all along the path between the initial and final points. This law holds true if the net work done by external nonconservative forces is zero. In situations where height varies and gravity is the driving force of motion, PE is converted into KE and vice versa.

6.6 Nonconservative Forces and the Work-Energy Theorem In the “real world” objects are affected by nonconservative forces such as friction. The work Wnc done by these combined forces is not equal to zero. Therefore, the difference between the final and initial total mechanical energies is equal to Wnc = Ef – E0 Check out Example problems 11 and 12 for great illustrations of how to use this equation when nonconservative forces are present and do work!

Helpful equation when problem solving 6.7 Power Ehh… Watts Up Doc? For many of us, the amount of time work is done in can be very important. While two objects can experience the same amount of work, the one accomplishing the work faster is more powerful. SI unit of power: joule/s = watt (W) Scalar quantity 1 horsepower = 550 foot pounds/ second = 745.7 watts Helpful equation when problem solving

Points to Remember! The amount of work done on an object is equal to a change in KE or PE The total mechanical energy of a system will equal KE + PE at any given point. Energy can neither be created nor destroyed, but can only be converted from one form to another. I am the most powerful because I finished my notes before you did! More work done in less time 