Static_Torques

docx

School

Mercyhurst University *

*We aren’t endorsed by this school

Course

101

Subject

Mechanical Engineering

Date

Apr 3, 2024

Type

docx

Pages

Uploaded by SuperNeutronOtter36

Static Torques Our goal for this lab is to understand the role that torques play in equilibrium scenarios. We have seen that an object can have forces acting upon it, even if it is stationary. The same situation applies to torques. There may be applied torques, but there is no overall motion of the object. In these cases, the torques or forces balance . Balanced scales are an example of an object which experiences torques but is in equilibrium. The weight on either side of the scale pulls on the lever arm at the top, but the entire apparatus is stationary if the weights are equal. This file is from Pixabay , where the creator has released it explicitly under the license Creative Commons Zero . Part I: Introductory Exercises Pictured below is a series of masses, hanging from a ruler. The ruler is pinned at its left edge so that it pivots there (black dot). In which of the four scenarios does the hanging mass exert the largest torque on the ruler? Please give your rational. The biggest torque is 2m at 4 is the as the force will be 8(mg). Practice sketching free body diagrams. In the bottom two scenarios (mass M), sketch the diagram for each. Remember, for the free body diagram of an ``extended object’’, you need to include the location of the forces along the object’s length.

Pictured below are two scenarios. In the first scenario, the mass is hung from a ruler that points horizontally. In the second, the ruler points at an angle above the horizontal. The rulers pivot from the point indicated at their left side. Which ruler experiences the greatest torque and why? The flat one because decreasing the angle decreases the torque Part II: Torques Acting On A Horizontal Lever Measure the mass of the aluminum meter stick: 1.489 kilograms Attach the aluminum meter stick to the pivot at its 10 cm mark as shown in Figure 1. Attach the plastic mass hanger to the meter stick at the 90 cm mark as shown in Figure 2. Figure 3 shows how to mount the meter stick to the table. There are quite a few steps to the assembly; they are outlined in the next paragraph. Mount the pivot/meter stick on the long aluminum rod and place the aluminum rod into the appropriate hole on the table. Attach a force sensor to a short rod, attach that rod to a mounting bracket, and mount the bracket to the top of the long aluminum rod. Tie the mass hanger to the hook of the force sensor. Make sure the force sensor and its mounting bracket are rotated to be in line with the meter stick. The string should pull directly outward on the hook of the force sensor. Adjust the height of the force sensor until the meter stick naturally lies horizontal. The level located on the pivot will help you with this. 2

Figure 3. The meter stick lies horizontally. The string pulls directly outward on the hook of the force sensor. 3

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Use another meter stick to measure the sides of the triangle formed by the apparatus. Use the base and height to determine the angle that the string makes with the horizontal. Be careful when measuring the base. Be sure to measure from where meter stick and aluminum rod intersect. Person Base (cm) Height (cm) tan θ θ (degrees) You 0.8 m 0.53 m 0.6 34.9 Your Partner Average Draw a free body diagram for the meter stick. Using the free body diagram, sum the torques acting on the stick. Solve the equation for the tension in the string. Show your work below. Same distance, just with the tension and pivot force meeting Using Capstone, we will measure the tension in the string. Start the program and configure the system to measure the force using the “Economy Force Sensor”. Release the tension in the string (by lifting up on the end of stick or unhooking the string) and zero the force sensor. Return the setup to its original configuration and record the force: 1.5 N Compute the percent difference between your measurement and your calculated value. Percent Difference: 17% Does it matter if you include the weight of the mass hanger (10 g, located at 90 cm) in you calculation? If you did not include it before, add its contribution to the torque and recompute your tension below. It matters because the mass of the hanger affects the tension. 4

By modifying your equations from above, determine where you would need to place a mass hanger (10 g) with a 200 g mass attached to it so that the tension in the string is increased to 3 N. In other words, at what centimeter mark would you need to place the additional mass to have the force sensor read 3 N? Show all of your work below. Slide the mass hanger off the meter stick so that a second one can be added at your predicted centimeter mark. Add the second mass hanger (the screw on this one should face upward) and reattach the first hanger/string at the 90 cm mark. Add the 200 g mass to the second hanger and verify that it is at the predicted location. Record the magnitude of the measured tension below. Calculate the percent error between your measured and predicted values. Double check your angle measurement and work if the percent error is larger than 5%. Measured Tension: 2.8 N Percent Error: 7.14% 5

Part III: Torques Acting On An Angled Lever Unhook the string from the force sensor and shorten where the loop is located. Reattach the string so that the meter stick is angle upward, as shown in Figure 4. Figure 4 The string, aluminum rod, and meter stick should make a right triangle. To ensure this is the case, we will compute the height (h) necessary to make this true. Measure the distance between along the meter stick (L). Be careful to measure from where the meter stick and aluminum rod intersect. Measure the distance along the string (d). Be careful to measure from where the corners of the triangle are located. Enter your values in the table below and compute the height necessary to form a right triangle. Adjust your height to this value. Person Hypotenuse: L (cm) Leg 1: d (cm) Height: h (cm) You .785 m .57 m .54 m Your Partner Average 6

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Determine the angles shown in Figure 4, using the sides of the triangle you just measured. θ 1 = 34.5 degrees θ 2 = 35.98 degrees Draw a free body diagram for the meter stick. Using the free body diagram, sum the torques acting on the stick. Solve the equation for the tension in the string. Show your work below. (0.76)F T sin(34.5) – (0.4)(0.1489)(9.8)sin(90) – (.34)(0.1)sin(35.98) F T = 1.31 Again, using Capstone, measure the tension in the string. Do not forget to zero the force sensor before collecting data. Compute the percent difference between your measured tension and the calculated tension. Double check your angle measurement and work if the percent error is more than 5%. Measured Tension: 1.9 N Percent Error: 45% Is the torque applied by the 200 g hanging weight and hanger larger or smaller than in the previous part, where the stick was horizontal? Explain your reasoning. It is smaller because we increased the angle of tension but decreased the angle for gravity. The pivot exerts a force that ensures that the net force is zero. Otherwise, the other forces would not balance! Determine the components of this force and then determine the magnitude and angle (measured from the horizontal) for this force. Y = 2.06, X = 1.9 it is not calculations, it is just words. 7

Part IV: Summary Questions 1) The meter stick, rod, masses, hangers, and string in this lab formed a system that was in static equilibrium. What are the two conditions that this system exhibited that shows it was in equilibrium? the torque has to be zero and the sum of the forces in the x and the sum of the forces in the y. 2) How did the gravitational torques change as the meter stick was moved from horizontal to a more vertical orientation? In what orientation does gravity produces the minimum amount of torque? Maximum? The gravitational torque decreased because the angle decreased, so when the gravitational angle is 0, that is when it would be at it’s minimum, the orientation would be straight up and down (vertical). The maximum angle between the force and the pivot would be at 90 degrees. 3) Imagine that, after completing the lab, you had removed the aluminum meter stick and tried to balance it on your finger. Suppose you showed that it balanced at its 52 cm mark (instead of the middle of the stick). What part of your calculations would be impacted? How would this affect your calculations: would you be over-estimating or under-estimating the tension in the string? r would be impacted because the torque is further out, the tension would be under-estimated because we are assuming the gravitational force is smaller than what is actually was. It is larger than originally thought. 8