1. Energy The ability to do work

2. Kinetic Energy (KE) The energy that an object has due to its motion. KE = ½ m v 2 –KE  m and KE  v 2 –Kinetic energy is a scalar quantity. –Energy units are the same as work units (kg*m 2 /s 2 ) = N*m = J F d v i = 0

3. Ex: A 7.00 kg bowling ball is moving at a speed of 3.00 m/s. How much kinetic energy does it have? Given: m = 7.00 kg v = 3.00 m/s v = 3.00 m/s Find: KE = ? KE = ½ mv 2 = ½ (7.00 kg)(3.00 m/s) 2 = 31.5 J

4. Ex. 2: What speed would a 2.45 g ping-pong ball need in order to have the same kinetic energy as the bowling ball ? Given: m = 0.00245 kg KE = 31.5 J KE = 31.5 J Find: v = ? KE = ½ mv 2  [(2 KE) / m] = v  [2(31.5J) / 0.00245 kg] =v 1.60 x 10 2 m/s = v

5. Gravitational Potential Energy (PE g ) Energy that is stored in an object due to its position above a surface. PE g = work done to raise mass m a distance  h PE g = mg  h Units = Joules ΔhΔh

6. Gravitational Potential Energy (PE g ) A reference level for determining  h must be determined (level where  h = 0). The exact path taken while changing  h is not important. If  h is positive, then PE g is positive. If  h is negative, then PE g is negative.

7. Ex: A 50 kg girl climbs a staircase of 15 steps, each step 20 cm high. How much gravitational potential energy did the girl gain? Given: m = 50 kg  h = 0.20 m (15 steps) = 3.0 m = 3.0 m Find: PE g = ? PE g = mg  h = (50 kg)(9.81 m/s 2 )(3.0 m) = 1.5 x 10 3 J

8. Elastic Potential Energy (PE e ) Energy stored in an elastic object (usually a spring) by deforming it (doing work on it). PE e = ½ kx 2 x = distance spring is deformed (stretched or compressed) k = spring constant: How resistant an elastic object is to being stretched or compressed (stiffness). Units = N/m Units = N/m (m 2 ) = N*m = Joules

9. Ex: A spring with a spring constant of 160 N/m is normally 14.0 cm long. How much energy is stored in it when it is compressed to 6.0 cm? Given: k = 160 N/m x i = 0.140 m x f = 0.060 m Find: PE e = ? PE e = ½ kx 2 = ½ (160 N/m)(0.140 m - 0.060 m) 2 PE e = 0.51 J

10. Mechanical Energy (E): The energy of an object due to its position or its motion. –Sum of kinetic energy, gravitational potential energy, and elastic potential energy. E = KE + PE = KE + PE g + PE e

11. Conservation of Mechanical Energy In the absence of friction, the total mechanical energy remains the same. E i = E f or KE i + PE g,i + PE e,i = KE f + PE g,f + PE e,f

12. Conservation of Mechanical Energy Mechanical energy is not conserved if friction is present. –Friction converts mechanical energy into other forms of energy (heat, etc.). –Total energy is always conserved.

13. Ex: A bird is flying horizontally 5.0 m above the water at a speed of 18 m/s when it drops a fish. How fast is the fish moving when it hits the water? Given: v i = 18 m/s Δh = 5.0 m Δh = 5.0 m Find: v f = ? E i = E f PE g,I + KE i = KE f mg Δh + ½ mv i 2 = ½ mv f 2 2g Δh + v i 2 = v f 2 √[(2g Δh) + v i 2 ] = v f √[(2*9.81 m/s 2 )(5.0 m)+(18 m/s )2 ] = v f v f = 20.m/s