WORK AND ENERGY Objectives 1) To determine the ideal mechanical advantage of an inclined plane. 2) To determine the work necessary to move a weight up an inclined plane. Required Equipment and Supplies Inclined plane Support stand Hall's carriage Set of spring balances 0-2.5 N, 0-5 N, 0-20 N 1-kg mass Protractor Meter stick with calipers Introduction An inclined plane is a simple machine. At times an object weighs too much for us to lift it. The inclined plane permits us to lift the object using a smaller force than its weight. However, the smaller force travels through a longer distance than the L actual vertical displacement of the object. The force required to pull an object up an inclined plane (at constant velocity) is equal to the h component of the weight of the object that is parallel to the plane and is given by mg sin 0, where mg is the 0 weight of the object and 0 is the angle the plane makes with the horizontal. The effect of friction is neglected. The work done by the force to move the object along the plane a distance, L, is given by W = (mg sin0)L This amount of work should be exactly equal to the work done to lift the object through the vertical height, h, and is given by W = mgh50 40 30 LEARNING PROGRAMMES. HIGHER CERTIFICATES. Uve OSTGRADUATE. 20 Date: Name: Section: The inclined-plane principle is applied in the use of ramps, stairs, screws, escalators, and wedges Procedures 1) Determine and record the weight of the Hall's carriage. 2) Calculate and record the weight of the Hall's carriage with the 1 kg mass. 3) Set the inclined plane at 10 . If you have questions concerning the use of the protrac- tor, ask the instructor before you proceed. 4) Mark the plane to show a starting and an ending point that are 1 meter apart. The carriage will be moving between these two points. h = 18 cm l = /meter 5) Determine the vertical rise between the two end points of the distance L along the incline plane. Record this vertical rise in the data table. 6) Put the 1 kg mass in the Hall's carriage and pull the system up the inclined plane using a spring balance. Record the spring balance reading as the ding as the force along the plane. 7) Increase the angle by increments of 10 (up to 509) and repeat st peat step 3. Keep the dis- tance along the plane constant as one meter, but be sure to record the vertical height each time since it will be different. Calculations 1) Calculate the ideal force up the plane, F = mg sin 0, for each of the five angles and record in the data table. ( 1. 4 35 ) ( 9.8) Sin ( 10 ) 2) Determine the IMA (ideal mechanical advantage) of the plane for each of the five angles. Use the Ideal Force calculated in question 1). Show below exactly how you make this determination. ( 1.LBS ) ( 9.8 ( 1. 435 ) Sin (10) = 5.76 3) Calculate the actual work done by the spring scale as you pulled the load up the plane. This is performed by multiplying the Force up the plane by the distance L N20 10 OCCUPATIONAL COURSES FREES. DIPLOMAS 15 Name: Section: Date: 4) Calculate the work needed to lift the load vertically through each of the five heights. 5) Calculate the percent difference between the work thru the distance L and the work thru the distance h. Questions 1) If the IMA can be expressed as the weight (mg) divided by the ideal force up the plane (mg sin 0) IMA = mg mg sine Reduce this ratio to its lowest term and comment on your results. 2) The IMA can also be expressed as the distance up the plane, L, divided by the vertical height, h.70 60 HV31 1MOHS 50 Section: Date: Name: IMA = L h Show that this ratio is the same as the reduced ratio determined in question 1). 3) Using the findings of questions 1) and 2), calculate the IMA for an angle of 18? Calculate the IMA for an angle of 640? 4) How do you explain any differences in the work along the plane and the work through the vertical height? 5) Why should the work along the plane be the same as the work through the vertical height? AMTloston.co.za fin@ 70 60 50 Name: Section: Date: Data Table 435. 18 kg Weight of Hall's carriage and 1 kg mass: 14 . 06 Newtons Distance along plane: meters Actual Ideal Vertical Work Percent Angle Work Force Force IMA Rise thru thru diff Force up mg sine h L h in work incline 10 3. 5 N 2. 4 4 N 5.56 / 18 cm 20 6. 5 N 4. 81 N 2.94 34 em 30' 8. 5N 7.03 N /1.96 slam 40' 10.5N 9.04 N 1.49 167 cm 50 12 N 10.7 7 N 1.30 7 7 cm 1.435