E p = mgh (if h i=0) E k = ½ mv 2 Ek is measured in Joules (J); m is measured in kg; v is measured in m/s. Energy Continued (E)

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1 nergy Continued () Gravitational Potential nergy: - e energy stored in an object due to its distance above te surface of te art. - e energy stored depends on te mass of te object, te eigt above te surface, and te strengt of te gravitational field. - On art, te strengt of te gravitational field (g) is 9.8 m/s 2. - In tis case, an object is raised some eigt above te surface of te art as sown below: Object, mass m =Δd Surface of art In te example to te left, te object wit mass m tat is acted on by gravity (g) is raised a certain distance above te surface of te art (). e cange in energy of te object is Δ = mg or p = mg (if i=0) p is measured in Joules m is measured in kg g is measured in m/s 2 is measured in m Note: sometimes in a word problem it is useful to select te lowest eigt in te problem as a reference point (call tat i = 0) and measure all canges in eigt (and subsequently canges in energy) in reference to tat point. is is called relative potential energy and will simplify calculations. Kinetic nergy: - e energy acquired by an object tat experiences a positive cange in velocity - A moving object as energy, and tat energy is proportional to te mass and te square of te speed. - e more mass an object as, and te faster it moves, te more energy it as, and te greater capacity it as to do work. - In tis case, energy is imparted to an object set in motion according to te following: Force Object, mass Δd = ½ mv 2 k is measured in Joules (J); m is measured in kg; v is measured in m/s.

2 Name: Practice Kinetic and Potential nergy 1. A crane lifts a 1500 kg car 20 m straigt up. a. How muc potential energy does te car gain? b. How muc energy does te crane transfer to te car? c. How muc work does te crane do? 2. A kg rubber ball drops from a eigt of 5.00 m to te ground and bounces back to a eigt of 3.00 m above te ground. a. How muc potential energy does te ball lose on its trip down? b. How muc potential energy does te ball regain on its trip back up? 3. A man on a flying trapeze stands on a platform 20m above te ground, olding te trapeze. e trapeze is 10 m long and is attaced to te roof 26m above te surface of te ground. e man swings down, and lets go of te trapeze on te upswing. He as a mass of 60 kg. Calculate is potential energy relative to te ground at te following eigts: a. 20 m (on platform) b. 16 m (bottom of swing) c. 18 m (lets go of trapeze) d. 9 m (alfway to ground) 4. Wat is te kinetic energy of a 0.50 kg ball trown at 30.0 m/s? 5. Wat is te mass of an object travelling at 20 m/s wit a kinetic energy of 4000 J? 6. Wat is te speed of a 1.5 kg rock falling wit a kinetic energy of 48J? 7. How muc work is required to accelerate a 150 kg motorbike from 10 m/s to 20 m/s? 8. A 0.50 kg rubber ball is trown into te air. At a eigt of 20 m above te ground, it is travelling at 15 m/s. a. Wat is te ball s kinetic energy? b. Wat is its gravitational potential energy relative to te ground? c. How muc work as been done by someone at ground level trowing te ball up into te air?

3 Mecanical nergy: - As we ave learned, it is possible to convert between one form of energy and anoter. - Specifically we will see tat it is possible to cange potential energy into kinetic energy and vice versa. - e sum of te potential energy and kinetic energy possessed by an object is called te mecanical energy. m = p + k = mg + ½ mv 2 - te law of conservation of energy states tat in a system witout friction, te mecanical energy is always constant. xample: A cild and is skateboard ave a mass of 60 kg. Starting from rest, e goes down a ramp wose vertical drop is 1.8 m. r a m p 1.8 m Wat is te boy's speed at te bottom of te ramp? Disregard te effects of friction. A) 9.0 m/s B) 6.0 m/s C) 3.0 m/s D) 2.0 m/s

4 Name: Date: Practice Questions Mecanical nergy 1. A football is kicked into te opposing team's zone by te Dragons' quarterback. Wic of tese graps sows te total mecanical energy,, of te football as a function of its eigt,? (Ignore te effects of air resistance.) A) C) B) D) 2. A cart is launced up a frictionless inclined plane. Wic of te following graps best represents te transformation of te different types of energy involved in te movement up te ramp? A) nergy C) nergy p p B) nergy D) nergy p p

5 3. A mountain bike rider starts at rest at point A, 200 m above te base of a mountain and descends te slope witout pedaling. (Friction is negligible) A 200 m B 150 m Wat is is velocity at point B, 150 m above te base of te mountain? Sow all of your work. 0 m 4. A small airplane wit a mass of 1000 kg, is flying at 60 m/s at an altitude of 250 m. 60 m/s 250 m Wat is te total mecanical energy of tis airplane wit respect to te ground?

6 5. A car wit a mass of kg arrives at te top of a ill 20 m ig at a speed of 10 m/s. At te bottom of te ill, te speed of te car is 20 m/s. 10 m/s 20 m 20 m/s How muc work was done on te car as it went downill? A) J B) J C) J D) J 6. Calculate te total mecanical energy in eac of te following situations? A) An automobile of mass 1000 kg travelling in a straigt line troug a distance of 1000 m at a speed of 30 m/s. B) C) D) An automobile of mass 1000 kg travelling in a straigt line troug a distance of 1000 m at a speed of 40 m/s. A small plane of mass 1000 kg flying at an altitude of 1000 m at a speed of 40 m/s. A small plane of mass 1000 kg flying at an altitude of 1000 m at a speed of 30 m/s. 7. An Olympic diver runs along a 3 m ig diving board, jumps into te air, and dives into te pool below. e 56 kg diver as a speed of 8.0 m/s te moment se leaves te diving board. At wat point is er gravitational potential energy at its maximum? A) Wile se is running along te diving board B) Wen se jumps into te air C) Just before se its te water D) Wen se is under water