Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Year 11 T1 Wk 8 Power Energy Bits and Pieces Falling objects If there is no significant air resistance then conservation of energy results in gravitational potential energy being converted into kinetic energy as an object falls. gain in KE = loss of GPE m gpe = mgh ke = 0 h v1 gpe = ke gpe = ½ mgh ke = ½ mv12 v2 gpe = 0 ke = ½ mv22 ke = mgh ½h Conservation of Energy Example Graphs of GPE and KE TOTAL ENERGY = GPE + KE GPE Energy KE 0 object dropped 0 Time object reaches lowest point Question A child of mass 40kg climbs a wall of height 3m and then steps off. Calculate the speed at which the child reaches the bottom of the wall. Child’s initial gravitational potential energy: GPE = m x g x h = 40kg x 10N/kg x 3m GPE = 1 200 J If air resistance is insignificant then all of this GPE is converted into kinetic energy KE = ½ x m x v2 1200 J = ½ x 40kg x (speed)2 1 200 = 20 x (speed)2 1 200 ÷ 20 = (speed)2 60 = (speed)2 speed = 60 speed = 7.75 m/s Choose appropriate words to fill in the gaps below: potential energy is the energy stored when an Gravitational ________ upwards This energy is released when the object is lifted ________. falls back to its initial position. object _____ Kinetic energy is the energy possessed by an object due to its speed and mass. If the mass of an object is ________ doubled its _______ kinetic energy doubles. If the speed is doubled the kinetic four energy will increase by ______ times. raised When a __________ object is released gravitational potential kinetic energy is converted into _________ energy. WORD SELECTION: falls speed four kinetic potential upwards doubled raised Power (P) Power is a measurement of how quickly work is done. power = work done time taken P= W t power, P is measured in watts (W) work done, W is measured in joules (J) time, t is measured in seconds (s) One watt is the same as one joule per second. Power is also equal to how quickly energy is transformed from one form to another. power = energy change time P=E t Power • The work done every second • The rate at which work is done or the rate at which E is consumed • • Power = Force × Velocity Question 1 Calculate the power of a motor that exerts a force of 40N over a distance of 2m for 10seconds. W=Fs = 40 N x 2 m work done = 80 J P=W/t = 80J / 10 s power = 8.0 W Question 2 Calculate the power of an electric motor that lifts a mass of 50 kg upwards by 3.0 m in 20 seconds. gain in GPE = m g h = 50 kg x 10 N/kg x 3 m = 1500 J g = 10 N/kg P=E/t = 1500 J / 20 s power = 75 W Power Example 3 • A student (50kg) climbs stairs of vertical height 7m in 9s. • Lifting force = weight: =mg=50x10=500N • Work done: Fxd = 500 x 7 = 3500J • PE gained = mgh = 50x10x7=3500J • Power = E/t = 3500/9 = 389 W Power Example 4 Power Example 5 • Crane lifts a load of 1200kg onto a building of height 12m. The carrier of the load has a mass of 300kg. What minimum power must the motor of the crane develop to lift the load in 15s? • Work done =PE gained (g=10N/kg) • mgh= 1500x10x12=180 000 • Power = work done/time • 180 000/15 = 12000w or 12kW Example 6 Example 7 Measuring a person’s power 1. Measure the weight, W of person using weighing scales. s total stairs height, h stairs of n steps person of weight, W =nxs 2. Measure the time taken for the person to run up a flight of stairs of height, h 3. Work done = weight x height =Wxh =Wxnxs 4. Power of the person = work done / time taken = (W x n x s) / t Example calculation Weight of person, W = 800N Time taken, t = 3.0 seconds s total stairs height, h stairs of n steps person of weight, W =nxs Stairs: number of steps, n = 12 height of step = 0.20m total stair height, h = 12 x 0.20m = 2.4m Work done = weight x height = 800N x 2.4m = 1920J Power = 1920J / 3.0s = 640W