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Kingdom Saudi Arabia, Riyadh Imam Mohammed bin Saud University College of science Physics department 281 physics – section 292 2nd term – 2011 3rd lecture – 3rd experiments Tr.Muneerah Alaqeel Conservation of mechanical energy Aim To find the final velocity of an object sliding an incline with constant acceleration using: 1. Energy conservation law. 2. Kinematics equations. Verify conservation of mechanical energy. Theory Energy is the ability to do work and is measured by Jouls. Mechanical energy has two different forms: Potential energy is the energy an object stores due to its position. The gravitational potential energy is given by: PE = m g h (1) Where m is the mass of the object, g is the gravitational acceleration and h is the height of the object. Kinetic energy is the energy of motion. The kinetic energy is given by: KE = (1/2) m v2 (2) An object held at some height h above the floor has no kinetic energy (v=0). If the object is dropped, it falls to the floor; as it falls, its speed and thus its kinetic energy increase, while the potential energy of the system decreases. In other words, the sum of the kinetic K and potential energies U – the total mechanical energy E – remains constant. This is an example of the principle of conservation of mechanical energy. The total mechanical energy E, of any isolated system of objects that interact only through conservative forces, is defined as the sum of the kinetic and potential energies, we can write E K U (3) We can state the principle of conservation of energy as Ei E f , and so we have Ki U i K f U f (4) Trolley xB xA d A hA Track B hB Figure1. The incline makes the trolley to move down with a constant acceleration If we apply the equation (4) to figure 1, we can write it as: K A U A KB UB (5) The velocity deduced from the principle of conservation of energy: vc 2 g hA hB (6) Where: g is acceleration of the gravity, hA initial height, hB final height. The velocity from the kinematics equations: vk 2d tB (7) Where: d is distance (m), tB the time needs to travel distance (s) Equipment Track – trolley – holding magnet – electronic stop clock – light barrier – cables. Procedure 1. Make the track inclined. 2. use the holding magnet to hold the trolley. 3. Connect the stop clock with a light barrier and put the light barrier at a certain distance and record the distance that the trolley should travel. 4. Measure the height at the beginning (hA) and at the end of the motion of the trolley (hB). 5. Release the trolley by pressing the START/STOP key at the electronic stop clock and find the time it needs to travel the distance three times and find the average time of traveling. 6. Reset the stopclock to zero by pressing the RESET key. 7. Move the light barrier to change the distance & height for 4 times then calculate the time in each distance as in step 5. (make the differences between each distance 10 cm at least) 8. Use the equations to find the final velocity. The two values should be equal. 9. Plot a graph between v k versus v c . ( v k is the y-axis and v c is the x-axis) Each axis should be labeled and appropriate units indicated. The graph should have a title. 10. 11. Determine the slope from the graph Find percentage error. 12. Verify conservation of mechanical energy by calculating potential energy & kinetic energy. 13. Remember to write your data in table. Table1 d (m) hA hB (m) (m) (m) t1 t2 (s) (s) t3 (s) t avr (s) vk (m/s) vc (m/s) (m/s)2 Table2 PEi (J) KEi (J) Ei (J) PEf (J) KEf (J) Ef (J) Ei = Ef (J) Homework Q1: what is potential energy? (Definition & equation) Q2: what is kinetic energy? (Definition & equation) Q3: what is mechanical energy? (Definition & equation) Q4: what is principle of conservation of mechanical energy? (Definition & equation) Q5: proof equation 6 & 7. Q6: Calculate the potential energy, kinetic energy, mechanical energy, velocity, and height of the skater at the various locations. Answer: 1. 0 J; 1.92 kJ; 1.92 kJ 2. 588 J; 1.33 kJ; 1.92 kJ; 6.66 m/s 3. 1.92 kJ; 0 J; 1.92 kJ; 0 m/s ; 3.27 m