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Dr. Jie Zou PHY 1151G Department of Physics1 Chapter 8 Potential Energy and Conservation of Energy

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Dr. Jie Zou PHY 1151G Department of Physics2 Outline Gravitational Potential Energy Conservation of Mechanical Energy Examples

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Dr. Jie Zou PHY 1151G Department of Physics3 Gravitational Potential Energy Gravitational potential energy U: The energy of a body due to elevated positions is called gravitational potential energy. U = weight height = mgh The gravitational potential energy is relative to the reference level and depends only on mg and the height h. Work done by a conservative force is equal to the negative of the change in potential energy. W c = - U = - (U f – U i ) = U i - U f

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Dr. Jie Zou PHY 1151G Department of Physics4 Example 1 Find the gravitational potential energy of a 65-kg person on a 3.0-m-high diving board. Let U = 0 be at water level.

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Dr. Jie Zou PHY 1151G Department of Physics5 Example 2 An 82.0-kg mountain climber is in the final stage of the ascent of 4301-m-high Pikes Peak. What is the change in gravitational potential energy as the climber gains the last m of altitude? Let U = 0 be (a) at sea level and (b) at the top of the peak.

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Dr. Jie Zou PHY 1151G Department of Physics6 Conservation of Mechanical Energy Mechanical energy E: The sum of the potential and kinetic energy of an object. E = U + K. Conservation of mechanical energy: In systems with conservative forces (such as gravity) only, the mechanical energy E is conserved. U i + K i = U f + K f. Assume there is no air resistance.

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Dr. Jie Zou PHY 1151G Department of Physics7 Conservation of Energy Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. The universe, in short, has a certain amount of energy, and that energy simply ebbs and flows from one form to another, with the total amount remaining fixed. Decrease in mechanical energy = E i – E f = 10 J = Thermal energy converted Mechanical E f = 90 J Mechanical E i = 100 J When Friction exists

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Dr. Jie Zou PHY 1151G Department of Physics8 Example 1 A player hits a 0.15-kg baseball over the outfield fence. The ball leaves the bat with a speed of 36 m/s, and a fan in the bleachers catches it 7.2 m above the point where it was hit. Assuming frictional forces can be ignored, find (a) the kinetic energy of the ball when it is caught and (b) its speed when caught.

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Dr. Jie Zou PHY 1151G Department of Physics9 Example 2 A 55-kg skateboarder enters a ramp moving horizontally with a speed of 6.5 m/s, and leaves the ramp moving vertically with a speed of 4.1 m/s. Find the height of the ramp, assuming no energy loss to frictional forces.

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Dr. Jie Zou PHY 1151G Department of Physics10 Example 3 If the height of the water slide is h=3.2 m, and the person’s initial speed at point A is 0.54 m/s, what is the horizontal distance between the base of the slide and the splashdown point of the person? d=?

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Dr. Jie Zou PHY 1151G Department of Physics11 Example 4 Suppose the pendulum bob has a mass of 0.33 kg and is moving to the right at point B with a speed of 2.4 m/s. Air resistance is negligible. (a) What is the change in the system’s gravitational potential energy when the bob reaches point A? (b) What is the speed of the bob at point A?

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Dr. Jie Zou PHY 1151G Department of Physics12 Potential Energy of a Spring U = (1/2)kx 2 k = the force constant (N/m) of the spring x = the displacement of the spring from its equilibrium position Example: If k = 680 N/m and x = 2.25 cm, then U = (1/2)(680 N/m)( m) 2 = J

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Dr. Jie Zou PHY 1151G Department of Physics13 Example Experiments performed on the wing of a hawkmoth show that it deflects by a distance of x = 4.8 mm when a force of magnitude F = 3.0 mN is applied at the tip. Treating the wing as an ideal spring, find (a) the force constant of the wing (b) the energy stored in the wing when it is deflected (c) what force must be applied to the tip of the wing to store twice the energy found in part (b)?

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Dr. Jie Zou PHY 1151G Department of Physics14 Homework See online homework assignment at Hand-written homework assignment: Chapter 8, Page , Problems: #34, 86.

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