Energy The ability to do work

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

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

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 = kg KE = 31.5 J KE = 31.5 J Find: v = ? KE = ½ mv 2  [(2 KE) / m] = v  [2(31.5J) / kg] =v 1.60 x 10 2 m/s = v

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

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.

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

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

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 = m x f = m Find: PE e = ? PE e = ½ kx 2 = ½ (160 N/m)(0.140 m m) 2 PE e = 0.51 J

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

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

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.

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