# Hookes Law Lab Hookes Law relates the amount

Hooke’s Law Lab Hooke’s Law relates the amount of force a spring exerts to the amount of distance a spring stretches. y = mx F=kx Force Spring Constant Stretch Distance

Let’s do an experiment… In our experiment, we will study the elastic properties of a spring and of a rubber band. • We will measure how closely they follow Hooke’s Law. • Our present interest is in whether or not the data will fit on a linear trend line. • A good fit indicates that the object (spring or rubber band) obeys Hooke’s Law. • Hooke’s Law states that the restoring force is a linear function of the displacement from equilibrium.

Our set-up

Hooke’s Law Lab A spring is said to “obey Hooke’s Law”, or be a “Hooke’s Law Spring” if the force is directly proportional to the stretching distance. For an ideal, Hookean spring, the spring stretches a certain distance for a certain force, regardless of whether the spring is “stretching out” or “stretching back”. This is NOT true for a rubber band! A rubber band does NOT obey Hooke’s law because the rubber band’s stretch depends not only on force, but whether the rubber band was “stretching out” or “stretching back”. After repeated stretching and unstretching, a rubber band loses its elasticity. An ideal metal spring does not.

Section 6 -1: Work What is the symbol for work? W Write a word definition for work. Work = (Component of Force || to Displacement)(Displacement) Write two formulas for work. W = F|| x W = F x cos( ) [ = angle between force and displacement] What are the units for work? Joules [J]

Section 6 -1: Work When is work equal to force times distance? When the force doing the work on an object is parallel to the displacement of the object. When does a force do positive work? Negative work? Zero work? Positive Work: When the force and the displacement make an acute angle. Negative Work: When the force and the displacement make an obtuse angle. Zero Work: When the force and the displacement make a perpendicular angle.

A. Positive Section 6 -1: Work B. Zero A man carries a box from point A and puts it onto a shelf at point D C. Negative along the path shown below. In the chart below, put a +, – or 0 to represent the sign of the work done by the man (WM), the work done by gravity (Wg), and the net work (Wnet) on the box during each path segment. D Fman x B C A Segment AB: Man lifts the box with constant velocity. Work done by the man’s force is: Work done by the gravity is: Net amount of work done is: Positive Negative Zero Fgrav Fnet = 0

A. Positive Section 6 -1: Work B. Zero A man carries a box from point A and puts it onto a shelf at point D C. Negative along the path shown below. In the chart below, put a +, – or 0 to represent the sign of the work done by the man (WM), the work done by gravity (Wg), and the net work (Wnet) on the box during each path segment. x D B C Fman A Segment BC: Man moves with the box with constant velocity. Work done by the man’s force is: Work done by the gravity is: Net amount of work done is: Zero Fgrav Fnet = 0

A. Positive Section 6 -1: Work B. Zero A man carries a box from point A and puts it onto a shelf at point D C. Negative along the path shown below. In the chart below, put a +, – or 0 to represent the sign of the work done by the man (WM), the work done by gravity (Wg), and the net work (Wnet) on the box during each path segment. D Fman x B C A Segment CD: Man raises box at constant speed to the top of the shelf. Work done by the man’s force is: Work done by the gravity is: Net amount of work done is: Positive Negative Zero Fgrav Fnet = 0

Section 6 -2: Work Done by a Variable Force How can the work done by a varying force be calculated? Be specific! A variable force can be represented by a force vs. displacement graph. To find work, take the area between the graph and the axis of a force vs. displacement graph.

Section 6 -2: Work Done by a Variable Force Example: A roller coaster car feels a force that varies with it position on the track as shown in the graph below: Find the work done when the object is displaced: From x = 0 to x = 5. Work = 12. 5 J F|| 5 0 – 5 5 10 15 20 x A. – 50 J B. – 25 J C. – 12. 5 J D. 0 J E. 12. 5 J F. 25 J G. 50 J

Section 6 -2: Work Done by a Variable Force Find the work done when the object is displaced: From x = 5 to x = 10. Work = 12. 5 J F|| 5 0 – 5 5 10 15 20 x A. – 50 J B. – 25 J C. – 12. 5 J D. 0 J E. 12. 5 J F. 25 J G. 50 J

Section 6 -2: Work Done by a Variable Force Find the work done when the object is displaced: From x = 5 to x = 15. Work = 0 J F|| 5 0 – 5 5 10 15 20 x A. – 50 J B. – 25 J C. – 12. 5 J D. 0 J E. 12. 5 J F. 25 J G. 50 J

Section 6 -2: Work Done by a Variable Force Find the work done when the object is displaced: From x = 0 to x = 20. Work = 0 J F|| 5 0 – 5 5 10 15 20 x A. – 50 J B. – 25 J C. – 12. 5 J D. 0 J E. 12. 5 J F. 25 J G. 50 J

Section 6 -3: Kinetic Energy, and the Work-Energy Principle What is kinetic energy? The form of energy that any moving object has. What is the symbol for kinetic energy? K What is the basic equation for kinetic energy? K = ½mv 2

Section 6 -3: Kinetic Energy, and the Work-Energy Principle Write the work-energy principle as both a formula and as a sentence. The net amount of work done on an object The sum of all of the works done by all of the forces on an object The work done by the net force on an object equals the object’s change in kinetic energy. W = K

Section 6 -3: Kinetic Energy, and the Work-Energy Principle Proof of the work-energy principle: The work energy principle. Net work is done by the net force. Net force is mass times acceleration. Plug this in to our equation. Distribute

Section 6 -4: Potential Energy What is potential energy? Energy that is “stored” in some form. What is the symbol for potential energy? U What is the basic equation for gravitational potential energy? Ug = mgh

Section 6 -4: Potential Energy Give the spring equation and explain what each symbol represents. F = –kx (Force) = (Spring Constant)(Stretch) Why is there a negative in the spring equation? To indicate that the direction of the force a spring exerts is opposite to the direction that the spring is stretched. Mr. Frensley calls this a “direction-carrying negative” or a “conceptcarrying negative”. It means that the negative sign is only there to remind us about direction; we do not use the negative when calculating the magnitude of the spring’s force!

Section 6 -4: Potential Energy What are the units for spring constant? Newtons/Meters [N/m] What is the equation for elastic potential energy? Us = ½kx 2 F kx x x

Section 6 -5: Conservative and Non-Conservative Forces Explain what a “conservative” force is. (1) A force that has a potential energy associated with it. (2) The work done by a C. F. depends only on the start and end position of the object (being worked on), not the path from start to finish. Give two examples of conservative forces. Force of gravity AND Force of a spring The work done by gravity/spring is the EXACT SAME as the potential energy equation for gravity/spring.

Section 6 -5: Conservative and Non-Conservative Forces Give an example of a non-conservative force. FRICTION FRICTION FRICTION FRICTION FRICTION Give an example of a force that never does any work. The normal force—it is always perpendicular to the motion of the object.

Section 6 -5: Conservative and Non-Conservative Forces Explain (in general) when potential energy increases and when it decreases. Potential energy decreases if the object GOT TO DO WHAT IT WANTS TO DO!!!!!1111 sin(90 o) Potential energy increases if the object WAS FORCED TO DO THE OPPOSITE OF WHAT IT WANTED TO DO!

Section 6 -6: Mechanical Energy and Its Conservation What is total mechanical energy? The sum of kinetic and potential energies for an object. What is a conserved quantity? A quantity that is neither created nor destroyed. A quantity that is the same at all times within a closed system.

Section 6 -6: Mechanical Energy and Its Conservation Under what circumstances is mechanical energy not conserved? Mechanical energy is not conserved if there is a non-conservative force (FRICTION) acting. Friction takes kinetic energy out of the system and turns it into thermal (heat) energy. State the principle of conservation of mechanical energy. The total mechanical energy initially in a system is equal to the total mechanical energy at any other time in the system. K i + Ui = K f + Uf

Section 6 -8: Energy Transformations and the Law of Conservation of Energy State the law of conservation of energy. In a closed system, the total energy (sum of all energies of all objects) remains constant. Explain what work is in terms of energy. Work is a change in any type of energy. Work is a transfer of energy from one object or form to another. Anytime any type of energy changes, work is done.

Section 6 -9: Energy Conservation with Dissipated Forces What is a dissipative force? A force that dissipates (takes away) mechanical energy. Explain thermal energy. Thermal energy is the energy an object with a temperature has. It is caused by the kinetic energies of all of the randomly-moving molecules in the object. What is the equation for the work done by (or energy lost to) friction? Wf = F f d (Work done by friction) = (Friction force)(Sliding distance)

Section 6 -10: Energy Conservation with Dissipated Forces What is the symbol for power? What are the units of power? P Watts [W] What is the basic equation for power (write using words and using symbols)? Power = (Work)/(Time) OR Power = (Energy)/(Time) P = W/t Give another equation for power (hint: it’s in example 6 -18). Power = (Force)(Velocity) P = Fv

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