PHY Lab 6: Work: Horizontal, Vertical, Inclined Plane

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1 Work: Horizontal, Vertical and with Inclined Plane And on the seventh day God ended his work which He had made: and He rested on the seventh day from all his work which he had done. Genesis 2:2 Introduction In Physics, work is performed on an object when a force acting upon the object causes it to move. If a force is acting upon an object and no movement occurs (such as holding a 20-pound weight motionless 3 feet off the ground), then no work is done on that object. Work may be occurring elsewhere (such as in the muscles), but not upon that object. At times, the amount of energy expended on an object may exceed the actual work output. In this case, work only refers to the amount of energy that actually contributed to the change in the object. Work is defined as the product of parallel force and distance. Mathematically: Work = Fd cos Θ ; where F = force, d = distance traveled and Θ is the angle between the force and direction of displacement. The unit of work is Newtons meters (N m), which is also called the Joule. Work is only done when the force exerted is parallel to the direction of movement. Suppose you push a shopping cart in the store. You are pushing horizontally, and the cart is moving horizontally or parallel to the force you are exerting. In this case the ϴ=0, the cosθ = 1, and the above work equation simplifies to: Work = Fd. But, consider a child trying to push a grocery cart and his force is at a 30 o angle to the cart. Excess energy is being expended. Work is only being performed by the portion of the force parallel to the cart s movement and the equation is: Work = Fdcos30. In Physics, simple machines offer a force advantage when pushing or lifting objects. A job that would typically take a great deal of work, can be changed into a task that requires much less effort when a simple machine is utilized. There are several types of simple machines: Inclined plane; screw; wedge; lever and wheel, and; a wheel and pulley system. If a mass had to be moved across the floor a certain distance and then lifted another distance, a certain total Work would have been done and a total Force expended. If an inclined plane had been used to cover this distance, what would the effect be on the Force? On the Work? This is what we will examine in this lab. See Figure 1. The Mass will be a 100- and 200-g hooked mass from your lab kit. A Spring Scale from the kit will be used to measure the Force (in Newtons) used to move the mass. Learning Objectives: Measure the work required to move a mass over a specific distance. Compare the work required to move the mass on horizontal, vertical and inclined surfaces. Examine the effect of the use of a simple machine, the inclined plane Catholic Initiatives in Math and Science, LLC All Rights Reserved 1

2 Materials Required: From Physics Kit Student Supplied Spring Scale, 500g/5 Newton Ramp (choose a long object for an inclined plane) 1 Weight, 100 g, with hook Measuring tape 1 Weight, 200 g, with hook Stack of books Protractor Masking Tape Safety Falling masses can cause injury. Make sure that the setup is secure in a clear area Keep hair, jewelry and loose clothing away from moving parts. Part 1: Moving Mass Horizontally Experiment 1. Prepare: Find a flat working surface such as a table Mark a starting point (START) on the table with a piece of masking tape Measure a point exactly 0.5 meters away from the START Mark this point with another piece of masking tape (END) Place 200-g mass on the 100-g mass; there is a bottom bar especially prepared for this use Now, hook the two masses onto the Spring Scale Total Mass = 300g 2. Experiment Place the leading edge of the first hooked mass at the START marked on the table Carefully pull the hooked mass at a steady speed from Start to Finish Note: It is important to keep the same speed in all trials Observe the force in Newtons required to move this mass this distance on the spring scale See Figure You may want to repeat this several time to ensure you have a consistent reading Record Force (in Newtons) obtained from the Spring Scale in Table A 3. Calculate Work (Actual Work) Using the Work equation, calculate the Work performed Note, since the movement is horizontal, and ϴ = 0, the work equation simplified to: Work = Force x distance 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 2

3 4. Calculate Work (Theoretical Work) First, you must calculate the theoretical force Knowing the combined mass of the Hooked masses, calculated force Force (N) = mass(kg) x m s 2 With this Force calculate Theoretical Work The Work equation is: W = fdcosθ 5. Calculate Percent Error Determine the Percent Difference between the Theoretical Work and Actual Work you obtained experimentally %Error = Experimental Theoretical x 100% Theoretical 6. Proceed onto Part 2: Moving Mass Vertically Part 2: Moving Mass Vertically In this part, you will place a stack of books and measure a vertical distance of 0.3-meters. The same mass (300 g) will be moved beginning from the point you ended in Part 1, and moving vertically 0.3-meters. The force applied will be measured with the Spring Scale. It is important to move with the same smooth speed that you moved with in Part I to obtain consistent results. See Figure below for Setup. Experiment 1. Prepare: Stack several books at the edge of the STOP place from Part 1 Measure and mark a vertical distance of 0.3-m from the table with tape on the books Place the 200-g mass on the 100-g mass Hook the two masses onto the Spring Scale 2. Experiment: Allow the masses to rest on the desk as you hold the spring scale vertically The spring scale should read zero Carefully, and at the constant speed you applied in Part A, move the spring scale vertically over the 0.3-meter distance 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 3

4 While lifting, observe the force (in Newtons) measured on the Spring Scale You may want to repeat this several times to ensure you have an accurate measurement Record the measurement in Table A 3. Calculate Work (Actual Work) Using the Work equation, calculate the Work performed Note, here the movement is vertical, and ϴ = 90 o The work equation is: W = fdcosθ 4. Calculate Work (Theoretical Work) First, calculate the theoretical force Knowing the combined mass of the Hooked masses, calculated force Force (N) = mass(kg) x 9.81 m s 2 With this Force calculate Theoretical Work The Work equation is W = fdcosθ 5. Calculate Percent Error Determine the Percent Difference as you did in Part 1 6. Proceed onto Part 3: Moving Mass Up Inclined Plane Part 3: Moving Mass Up Inclined Plane Find a long object to be a ramp, that will span the distance between the START point in Part 1 and the ending point on the stack of books in Part 2. This ramp could be a meter stick, a cardboard box, or a board, etc. 1. Prepare: Place one edge of the ramp at the starting (START) marker of Part 1 Place the second edge on the stack of books at the 0.3-meter vertical mark With the protractor ensure that the angle is 30 o Place the edge of 300-g masses on the Spring Scale at the START mark The setup should resemble the figure to the right: 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 4

5 2. Measure and Record: Measure the Start and Stop distance the mass will travel up the ramp under Displacement column 3. Experiment: Carefully, and with steady speed, move the spring scale and mass up the incline. As you move, observe and record the force (Newtons) required to move the mass. You may want to repeat several times to ensure you have an accurate measurement 3. Calculate Work (Actual Work) Using the Work equation, calculate the Work performed Note, here the movement is inclined, and ϴ = 30 o The work equation is: W = fdcosθ 4. Calculate Work (Theoretical Work) First, calculate the theoretical force Knowing the combined mass of the Hooked masses, calculated force Force (N) = mass(kg) x m s 2 With this Force calculate Theoretical Work The Work equation is W = fdcosθ 5. Calculate Percent Error Determine the Percent Difference as you did in Part 1 6. Perform the Data Analysis and Conclusions 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 5

6 Data Organization θ Displacement (m) 0 o 0.5 m 90 o 0.3 m Table A: Moving Mass Horizontally ACTUAL FORCE (N) Force measured on Spring Scale ACTUAL WORK (J) Work (W=Fd) Theoretical FORCE (N) F = mg (g = 9.81 m/s 2 ) Theoretical WORK (J) W = fd %Error 30 o Combined mass of the Hooked Masses = 300 g Data Analyses and Conclusions 1. Compare the results of your Force data for moving 300-g horizontally, vertically, and then up an inclined plane. a. How did the horizontal displacement compare with vertical displacement? What accounts for the difference, if there is any? b. How did the horizontal and vertical displacements compare with the inclined plane displacement? What accounts for the differences, if there are any? c. Compare the material of the table with the material of the ramp. Would there be any difference due to friction in moving the mass across the table as compared to up the ramp? 2. Compare the results of your Work data for moving 300-g horizontally, vertically, and then up an inclined plane. a. How did the horizontal displacement compare with vertical displacement? What accounts for the difference, if there is any? b. How did the horizontal and vertical displacements compare with the inclined plane displacement? What accounts for the differences, if there are any? 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 6

7 3. You are given the task of moving a mass from a starting point as shown below in Figure 1 to the top of a stack of books. You have two choices: A) Push/Pull the mass horizontally over distance-d1, and then lift the mass up distance-d2, or; B) Use an inclined plane to push/pull the mass over distance-d3. Use YOUR data to answer the following: a. Would Option A or Option B use the greater amount of force? Explain using your data as proof. b. Would there be more work in Option A or in Option B? Explain using your data as proof. 4. Why is the advantage of an inclined plane? To answer this, use both your data and your sense of effort of moving the mass to help explain. 5. The Inclined Plane: You must push a piano up an inclined plane into a moving truck. You have three ramps to choose from: 20-foot long ramp; 10-foot long ramp; 5-foot long ramp. a. Which ramp would be at the greatest angle to the ground? b. On which ramp would you have to travel the shortest distance with the piano? c. Which ramp would make it easier to push up the piano? Explain. d. In order to use less effort to push the piano, a trade-off has to be made. What is this trade-off based on your answers to the above questions? 6. Simple Machines: a. Does a simple machine, such as the inclined plane, alter the amount of WORK a person must do? b. What is the advantage of a simple machine? 7. Give two applications of the inclined plane you observe around you. 8. Review your data and state your conclusions here Catholic Initiatives in Math and Science, LLC All Rights Reserved 7