PHYSICS 220 LAB #5: WORK AND ENERGY

Transcription

1 Lab Section / 33 pts Name: Partners: PHYSICS 0 LAB #5: WORK AND ENERGY OBJECTIVES 1. To get practice calculating work.. To understand the concept of kinetic energy and its relationship to the net work (the Work-Energy Theorem). 3. To calculate the coefficient of friction. OVERVIEW The same experiment as in Lab #4 will be analyzed using the concepts of work and energy, instead of Newton s laws. Recall that in the last lab a dropped mass dragged a cart forward via a rope over a pulley. PART ONE: Work In this section, you ll use the Work-Energy Relation to create the equations that describe a falling mass pulling a cart along a track. In the next section, you ll plug in actual data. Theory The work done by a force on an object depends on how much the force points in the direction that the object moves. For a constant force, the work is related to the size of the force (F), the length of the displacement ( r), and the angle between the displacement and force vectors (θ) by W = F r cos θ F r θ r If the force and the displacement are somewhat in the same direction ( θ < 90 ), the work will be positive and if they are somewhat in opposite directions ( θ > 90 ), the work is negative. If the force is perpendicular to the displacement ( θ = 90 ), the work is zero. The kinetic energy of an object is related to its mass and speed (the direction of the motion does not matter): KE = 1 mv

2 According to the Work-Energy theorem, the total (or net) work done on a system by external forces is equal to the change in the system s energy. Forces between objects within the system are internal forces, so they are not included. We ll consider the situation shown below: a falling mass pulling the cart+probe. We ll define the system as System = cart+probe + falling mass. 1. On the diagram below, clearly draw and label all of the forces on the cart and on the falling mass (including the frictional force on the cart). 3 pts 3 pts Question: What forces do no (zero) work on the system? Why? Steps through 7 walk you through writing the work-energy relation for this system in terms of the variables below. Then you ll solve it for µ. In this part, you will not be using any data. All answers should be in terms of the following variables: m cp = mass of cart & probe m f = falling mass g = gravitational acceleration µ = coefficient of friction v i = initial speed (not zero!) v f = final speed r = distance cart moves while speeding up Page

3 . Write an expression for the work done by gravity on the falling mass. (Be careful to include the appropriate sign.) W grav = 3. Write an expression for the size of the frictional force on the cart F frict = 4. Write an expression for the work done by the frictional force. (Be careful to include the appropriate sign.) W frict = 5. Write an expression for the change in kinetic energy for the system (the cart and the falling mass). KE = 6. Use the Work-Energy theorem to write an equation relating the expressions above Question: Why don t you need to worry about the work done by tension when applying the Work-Energy theorem? Page 3

4 7. Solve the equation above to get an expression for the coefficient of friction. µ = Experiment Now you ll use the equation you ve derived to analyze the real things a falling mass pulling a cart along a track. 1. Transfer the time, velocity, and position data from Lab 3 onto the table on the next page or gather some new data. If it s gather new data that you choose, here s what you do. a. Be sure a force probe is plugged into CHANNEL 1 of the Lab Pro and a motion detector is plugged into the DIG/SONIC 1 port. The force probe should be on the ±10 N setting. b. Open the file called Force and Motion (in Physics Experiments / Physics 0 1/ Newton s Laws folder on the computer desktop) to start with a set up to measure velocity, acceleration, and force. c. To calibrate the force probe, select Calibrate from the Experiment menu, select CH1: Duel Range Force (N), and click Calibrate Now. For Reading One, leave the probe unloaded, enter 0 N and hit Keep. For Reading Two, hang a 100-g mass from the probe and enter its weight: 0.98 N, then click Keep. Finally, hit Done. d. Set up the track, pulley, cart, string, motion detector, force probe, and a hooked 100 g (0.1kg) mass as shown below. The string should be approximately horizontal and the hanging mass should be close to the pulley when the cart is near the other end of the track. Page 4

5 3pts e. With mass hanging, click Collect and release the cart after the motion detector starts clicking. Be sure that the cable from the force probe isn t seen by the motion detector and doesn't drag. Catch the cart before it hits the pulley! Repeat until you get fairly smooth graphs of the motion. Note: You may need to adjust the motion detector s up-down angle and switch it to wide range (switch on top). f. To acquire the velocity values, click on the velocity plot, and select Examine under the Analyze menu. As you move the cursor across the Velocity plot, velocity and time values will be displayed. Record a velocity and time pair from soon after the cart starts moving and record one from a little before it peaks. The initial velocity should not be zero. g. Convert the Acceleration plot to a Position one by right-clicking on the vertical axis label and selecting Position. Then follow the same procedure as for the Velocity. Be sure to collect positions for the same times as your velocities. Okay, either from Lab 3 or from new data, fill in the table below. ti = s vi = m/s xi = m tf = s vf = m/s xf = m Mass of Cart & Probe: m cp = Falling Mass: m f = 0.1 kg. Calculate the size of the displacement of the cart (and the falling mass) between times ti and tf (include units). r = Page 5

6 3. Use the expression from Part One to calculate a numerical value for the cart s coefficient of friction. pts µ = Question: Occasionally, the data will result in a negative value for µ. From the expression in Part One for the work done by friction, why should µ always be positive? PART TWO : Potential Energy Now you ll employ the Conservation of Energy to analyze a simulated mass hanging from a spring. Theory Choosing your System. When using the Work-Energy relation, it s important to choose your system, i.e., whose energy you re tracking. Just like a choice of coordinate system, this choice is arbitrary, but once made, you ve got to stick to it. Take for example a mass dangling from a spring. If the mass is the system, then the only form of energy it can have is kinetic (we ll ignore heating and such), the spring and Earth do work on the mass by pushing and pulling on it. Then again, if you call the mass+spring+earth your system, then it can have kinetic energy, elastic potential energy (in the spring) and gravitational potential energy. For this exercise, let s say System = mass+spring+earth Forms of Energy. This system has three forms of energy that change as the mass bobs up and down, those changing energies are 1 Kinetic: K. E. = ( mv ) Gravitational Potential: P. E. grav = ( mgy) Page 6

7 where we ll take up as the positive y direction 1 Elastic Potential: P. E. = ( k s ) elastic sp Where s is how much the spring is stretched and ksp is the spring constant which quantifies how stiff the spring is. Conservation of Energy. Ignoring friction and heating, this system is isolated, i.e., there s no work getting done on it or by it. So E = W reduces to E = 0. So, we say that energy is conserved. system In terms of the different forms of energy, this can be written as E = K. E. + P. E. + P. E. = 0 grav elastic Or ( ) ( ) ( ) 1 1 mv + mgy + k s = 0 E = sp Simulation Now, you ll use the Conservation of Energy relation to determine the maximum speed of a simulated mass bobbing on a spring. Set-up 1. Launch PhET from the Start Menu. Click the Go to Simulations Button, and select Work, Energy, and Power from the left menu bar. Finally, select the Masses & Springs simulation.. Remove friction by sliding the friction bar to none. 3. Set the program to display energy by clicking the Show Energy of 1 button. 4. Hang the 50 gram (0.5 kg) mass from Spring 1 without plucking it, i.e., just put the mass on the end of the spring and don t drag the mass down (of course, it will pull the spring of its own volition). The mass should bob up and down. Qualitative Analysis Note: to slow the mass s motion, you can select 1/16 time instead of real time display. That may help you to analyze the system. Page 7

8 5. How does the Total Energy behave as the mass bobs up and down? 6. Where is the mass when the Gravitational Potential Energy is greatest? Select all those that apply. a. Bottom b. Middle c. Top 7. Where is the mass when the Elastic Potential Energy is greatest? Select all those that apply. a. Bottom b. Middle c. Top 8. Where is the mass when the Kinetic Energy is greatest? Select all those that apply. a. Bottom b. Middle c. Top Quantitative Analysis 9. Given the spring constant, ksp = 9.8 kg/s, the hanging mass, and g, calculate a value for the maximum velocity of the mass. Suggestions a. You can drag the ruler down so its top is at the dashed line the bottom of the spring when fully compressed. If you take this as the negative y-axis, then in this coordinate system y = s = v = 0 when the spring is fully compressed. i. Note: since the ruler is the negative y-axis, where it reads 5 would be y = - 0.5m. ii. Note: the program s energy display corresponds to a different choice of coordinate systems, so you might as well turn off the energy display. b. Applying the conservation of energy requires you compare energies (gravitational, elastic, and kinetic) at two places. It s awfully convenient to choose one place to be at s = y = v = 0, and the other to be where v is maximum (for that s your target value). Page 8

9 1 1 c. Be careful, P. E. = ( k s ) = k ( s ) 1 not ( s) elastic sp sp k sp. 3pt vmax = m/s Page 9