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Work – Energy Introduction to Physics 105 6/98 Name _____________________Conf________ Partner’s Name ________________________ Equipment cart, track, hanger and masses, photogate, card, cushion, pulley, meter stick, lab jack, spring, lab stand, string Purpose: Investigate work and energy relationships by doing three different experiments. Data: Show your work in the Data and Calculations space. Attach additional work and graphs to lab. Include all steps, labels and remember your units. Definitions Gravitational Potential Energy = mgh Kinetic Energy 1 2 mv 2 Potential Energy of a Spring Percent Difference 1 2 kx 2 xy 100 y Total Mechanical Energy, E E = PE + KE Part 1 m g h m v k x x y mass acceleration due to gravity height above reference level mass speed spring constant spring stretch second value first value(most reliable value) PE = Potential Energy KE = Kinetic Energy Gravitational Potential Energy Purpose In this experiment you will compare the gravitational potential energy stored in a hanging mass to the kinetic energy that the system receives. Procedure 1. Set up the equipment as shown in Figure 1 on a level track. cart photogate timer M card 20 g track mass - m cushion Figure 1 Clark College Physics Dept –1– h Work – Energy 6/98 2. Place a total (mass + hanger) of 20 g on a the end of a string . This is mhanger. Record in the space below. 3. Determine the mass of the cart and the card. This is mcart. Record below. 4. Determine the mass of the system. Msystem = mcart + mhanger. Record below. 5. Pull the cart back so that the hanging mass is approximately 30 cm above the cushion. Measure the exact height to at least one decimal place. This is height h. Record below. 6. Compute the initial potential energy of the mass relative to the cushion. Remember : PE = mhanger g h Show calculations and record below. 7. Let the mass drop and measure the final velocity of the system using a photogate timer (velocity = [card length]/time). Compute the final kinetic energy of the system, using Msystem. The cart should go through the photogate just after the mass hits the cushion. Show calculations and record below. 8. Calculate the percent difference between the initial potential energy of the mass (mhanger) and the final kinetic energy of the system (Msystem). 9. Is total mechanical energy conserved? If not do your results suggest that energy was lost to friction? Explain. Data and Calculations mcart= (kg) Msystem=mcart+mhanger= h= PE = mhanger g h = Card length = (kg) (meter) (Joule) Time = (sec) Speed = (m/s) 1 2 KE mv2 = % difference = Clark College Physics Dept (meter) –2– (Joule) Work – Energy Part 2 6/98 Potential and Kinetic Energy Purpose In this experiment you will compare the gravitational potential energy stored in the cart to the kinetic energy that the cart receives by changing heights. Procedure 1. Set up the equipment as shown in Figure 2, on a inclined track. Note that the string from part 1 has been removed. Measure the height of the cart above the table at positions 1 and 2. h1 = _______ h2 = ________ Photogate timer 1 2 Figure 2 2. Measure the mass of the cart and compute the potential energy (PE) of the cart at each of the two positions. Clearly label data and show calculations here. Position 1 Position 2 PE=M g h (J) 1 KE mv2 (J) 2 Total Energy (J) 3. Place the cart at position 1 and release it from rest. Use the photogate timer to calculate the velocity of the cart at position 2. Remember : v = x / t, where x = length of the card and t = time from the photogate. Position 1 Position 2 ********* Time, t(s) Card length, x (m) ********* 0.0 Speed, x/t (m/s) 1 4. What is the kinetic energy KE mv2 of the cart at positions 1 and 2? Record in the table above. 2 5. Calculate the TOTAL mechanical energy, E = KE + PE of the cart at positions 1 and 2, and record in the table above. Is total mechanical energy conserved? Explain. Clark College Physics Dept –3– Work – Energy Part 3 6/98 Stored Energy Purpose In this experiment you will compare the potential energy stored in a spring to the kinetic energy that the cart receives when pulled by the spring. Procedure 1. Find the spring constant as explained below. Set the spring in the lab stand as shown. Measure the spring’s initial length (L0) when no force is applied. Apply a force of 1.96 N to the spring by spring hanging a 200 g mass on the end of the spring. L0 = cm Measure the length of the stretched spring. Calculate the stretch (L – L0) for this force. Put your values in the table below. Force (N) Lo (m) Figure 3 Length (m) Stretch (L-Lo For an ideal spring the stretch is directly proportional to the applied force. That is F = k(stretch)= kx. This relation between stretch and force is called Hooke's Law. The spring constant (k) can be calculated by dividing the force by the stretch. Do this to calculate k. k=F/x=________________ Spring Constant, k=_____________________ Clark College Physics Dept –4– Work – Energy 2. 6/98 Make sure that the track is level. Place a cart on the track and attached it to a spring as shown. Make sure that the photogate timer is to the right of the card when the spring is unstretched and that there is enough string between the end of the track and the spring so the cart can easily glide through the photogate after the spring gets to its unstretched position. Pull the cart back stretching the spring. Measure the total spring stretch, x. cart M photogate timer card track 30 cm of string stretched spring Figure 4 3. x= 4. Calculate the potential energy stored in the spring when it is stretched. (m) k= (N/m) Spring PE 1 kx 2 2 PE= (J) Position the photogate timer so you can measure the velocity of the cart right after the spring becomes unstretched. Unstretched position Time, t (s) Card length, x (m) Speed, x/t (m/s) 5. Calculate the kinetic energy of the cart. 1 KE mv2 2 6. Unstretched position (J) Compare the initial potential energy stored in the spring with the kinetic energy of the cart. Clark College Physics Dept –5– Work – Energy 6/98 Questions 1. If the photogate timer ran slow. That is, measured too short a time, would the kinetic energy measured using the timer be too high or too low? 2. If there were friction in Part 3, would the potential energy be greater than or less than the kinetic energy? Clark College Physics Dept –6–