PHYSICS 220 LAB #3: STATIC EQUILIBRIUM FORCES
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1 Lab Section M / T / W / Th /24 pts Name: Partners: PHYSICS 220 LAB #3: STATIC EQUILIBRIUM FORCES OBJECTIVES 1. To verify the conditions for static equilibrium. 2. To get practice at finding components of forces. Theory An object is in static translational equilibrium if it isn t translating or going to start translating, i.e., it has zero velocity and zero acceleration. Through Newton s Second Law, the latter means that there is no net force on the object. This means that the sum of the forces in each component direction is zero ( F x = 0 and F y = 0 ). The force transmitted through a string, i.e. tension, points along the string. The force of the Earth s gravitational pull on an object, i.e. the object s weight, is w r = mg r, where m is the mass of the object and g r is the acceleration it would have if in free-fall: g = 9.8m/s 2. The x and y-components of a force in the x-y plane are related to the force s magnitude and direction (measured from the x-axis) by F x = F cosθ and F y = F sin θ. PART ONE: The Force Table You ll determine the one force necessary to balance two others that pull the ring in the middle of the force table. 1. Carefully level the force table. Hang 300 grams from one string at 0 relative to the x-axis and 200 grams from another string at 120 relative to the x-axis. Including the hanger s mass.
2 2pt 2. Record the masses and angles below. Don t forget to include the mass of the hangers. m2 = θ2 = T2 = m3 = θ3 = T3 = Question: Draw a free-body diagram for a hanging mass while it is hanging stationary from a string (That s a diagram featuring only the object and arrows representing the forces applied to it; the lengths of your force vectors should accurately represent their relative sizes). See figures in Ch. 4 of the text for examples of free-body diagrams. Explain the relative sizes of the forces using one of Newton s Laws. 2 pts Hanging mass 3. Calculate the magnitudes of the tensions in the two strings and enter them above. 4. Imagine the ring is perfectly centered on the force table (it will be soon), and assume the tensions on the ring are approximately horizontal (of course, they must actually be slightly upward to hold up the ring). On the following grid (top of the next page), carefully draw and label the horizontal forces on the ring due to the two strings as seen from above. Use the x-axis as 0. The lengths of the vectors should approximately represent the relative sizes of the forces. Page 2
3 y (90 ) 3pts x (0 ) 5. Using the principles of equilibrium, determine magnitude and direction (angle relative to the x-axis) of the third tension that would be necessary to balance the other two, and thus hold the ring in the center of the table. Then determine the hanging mass needed to provide that tension. Show all of your work clearly (label things, don t just write down a bunch of numbers!). Note: inverse trig functions return the corresponding acute angle; you ll need to add the appropriate factor 90 to get the angle in the correct quadrant. 4 pts T1 = θ1= m1= Page 3
4 6. Now s the moment of truth, position the third string and load it with the mass you ve calculated (remember that the hanger itself contributes to the mass.) Adjust the mass and angle for this third string until the ring hangs as near center as possible (don t change the masses or angles of the other two strings.) Question: How does this mass compare with that you d expected? Calculate percent error: (1 expected/actual)*100% 1 pt PART TWO: The Crane Now for a more interesting geometry, you ll calculate the components of the force the clamp must be exerting at the bottom of the crane to hold it steady. 1pt 1. Use the spring scale to measure the weigh of the beam (i.e., take the contraption apart and let the beam hang from the scale while you hold the scale don t leave the foot of the beam in the clamp or let the beam rest against anything that would affect the weight reading. Note: the scale it reads in grams, so you will need to convert that to Newton s. W = 2. Set up the stand clamps, string, beam, and force probe as shown below. Hang a 500-gram mass by a string from the end of the beam. Page 4
5 hook Spring Scale θ 1 clamp beam θ2 2pts 1pt 3. Measure the angles between the beam and each of the strings. θ1 = θ2 = 4. Use the spring scale to measure the tension on the string. T = 5. Carefully sketch the beam and all of the forces on it. Be sure to indicate where the forces act and their directions. (Recall that the beam s own weight can be thought of as acting at its center of mass.) 3pt Page 5
6 Questions: What force on the beam haven t you measured? Where does it act? 1pt 6. Determine the horizontal and vertical components of the unknown force acting at the axis. Show all of your work clearly. Note: The angle that the tension force makes with the horizontal is θ θ 2 4pts Page 6
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