Physics+1200+Lab-8

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Ohio University, Main Campus *

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1200

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Physics

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Jan 9, 2024

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7

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Physics 1200 - Lab#8 Page 1 of 7 Name ______________________________ Partner(s): ___________________________________________________________ Lab 8: Rotational Kinematics and Rotational Equilibrium Note: Even though the SI unit for torque is m·N (length in m, and force in N) throughout this lab (to keep your calculations simple and tidy) you will not convert the mass grams into weight and call it simply gm-weight. You also will not convert cm into meters. In this case torque will be given as (cm·gm-w).
Physics 1200 - Lab#8 Page 2 of 7 Activity 1: Mass of the meter stick, and its Center of Gravity a) Use the scale and measure the mass of the meter stick: _____________ grams b) Finding center of gravity of meter stick. For a point mass the force of gravity (i.e., weight) acts at that single point. However, for an extended object like a meter stick the force of gravity acts at every point on it but we can assume that the force of gravity acts at a single point and that is called the center of gravity (CG). CG of an object depends on its shape and distribution of mass. Quick method to find the meter stick’s approximate position of center of gravity: Place the meter stick’s two ends on your two index fingers and let the meter stick stay horizontal. Now move your fingers slowly to the middle of the meter stick while maintaining the horizontal orientation of the meter stick until your two index fingers touch each other. Meter stick’s mark on the midpoint of your two index fingers is the center of gravity of the meter stick. Now you know the approximate CG of the meter stick. You can find it more precisely as follows. Tie a string loosely around the meter stick close to its approximate CG and hang it from the dowel on the stand as shown in the Fig.1 below. Adjust the position of the meter stick until it balances horizontally. Position of the string on the meter stick is the CG of the meter stick and record it here ________________ cm. Is it close to your approximate method value? Yes No 134 50 O
Physics 1200 - Lab#8 Page 3 of 7 Activity 2: Static equilibrium of the meter stick a) Predict where a 90 g mass must be hung on the meter stick to keep it horizontal. Meter stick has holes at 30 cm mark and 60 cm mark. Insert the dowel at 30 cm hole on the meter stick. Determine at what position on the meter stick you need to hang the 90 g mass (including hangar mass) to maintain a horizontal orientation. Draw a free-body diagram of the meter stick showing ALL forces acting on the meter stick and their positions in the Fig-2 above. Indicate your choice of axis of rotation. Verify if the meter stick maintains horizontal equilibrium by hanging the 90 g mass at the calculated position. Does it balance? Yes No b) Repeat the above procedure by attaching the meter stick to the dowel at 60 cm position, and predict where a 70 g mass (including hangar) must be hung on the meter stick to keep it horizontal. Does it balance? Yes No 0cm O E tty am so cm 0
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Physics 1200 - Lab#8 Page 4 of 7 Activity 3 Lab Challenge: Walk the plank (meter stick is the plank) You are the captain of a pirate ship and are about to demonstrate to your crew how to set up a plank in stable equilibrium. Follow the setup instructions below and arrange the meter stick as shown in Fig-3 below. The meter stick is supported by a rod in a dowel that passes through the 60.0-cm position on the meter stick. Tie a string through a hole at the 30.0-cm position and pass the string over two pullies, then hang a 350-gram mass (including hangar mass) on the end of the string. Note that at this point the meter stick is not in balance. Place a jack stand under the meter stick, as shown in the Figure-x (at the right end of the stick to support it). Adjust the jack height such that the stick is horizontal. Make sure two pullies are in line. Do NOT add masses at P and S until you finish your lab challenge calculation as specified below and checked by your lab instructor. Fig.3: P and S are the approximate locations of the pirate captain and the seagull, respectively.
Physics 1200 - Lab#8 Page 5 of 7 Now, as the pirate captain (mass = 150 g including hangar), you walk the “plank” to demonstrate to your crew that everything is stable. You walk to position P starting from the dowel. Even though you can walk further without tipping the plank you stop there at P anticipating a flying seagull to land at mark S. Ask your lab instructor for the mass of the seagull and its landing position S on the plank. Mass of Seagull: ________________ Position of Seagull: ________________ Measure the angle between the plank and the tension force in the string using a protractor as suggested in the Fig-4 below. Fig. 4 This is your lab challenge: Based on the information you have about the plank and all the forces acting on it including seagull mass, determine (using the static equilibrium conditions) the location P where pirate captain can stand and balance the plank horizontally (without jack support). First do the calculations and show your result to your lab instructor before attaching the masses P and S to verify your calculation. Use the meter stick in Fig.5 below to draw a free-body diagram. Show all the forces acting, at different positions, on the meter stick (including its own weight force). Choose a location for the axis of rotation and indicate that location with a small circle. ( Hint: the dowel also exerts a force on the meter stick: since you do not know what this force is, what would be an advantageous location for the axis of rotation? ) 50g 35cm 650
Physics 1200 - Lab#8 Page 6 of 7 Fig-5: Torque, τ = r × F × sin θ (torque is identified with a positive or negative sign. If a torque causes counter-clock-wise acceleration it is positive, and for clock-wise acceleration it is negative). Collect the following values for each force from the above free-body diagram and enter in the table below to calculate the ± torques they produce. r is the distance from axis of rotation to the point where the force is applied. F is magnitude of the force. θ is the angle between r and line of F . Exercise 2: Solve the problem and determine the position of the pirate that will keep the setup in balance (hint: when the setup is in balance the net torque = 0). At what position will you place the pirate? _________________________ Distance, r cm Force, F (gm-w) Angle, θ Torque, τ (cm·gm -w) = ± r × F × sin θ Plank Seagull Dowell Pirate 350-g mass Mfs of t dog Mag 10 134 1800 1340 25 50 2700 1240 0 149 1730 710 46 150 2700 6226 30 350 650 9516 45cm from the pivot point
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Physics 1200 - Lab#8 Page 7 of 7 Your lab instructor checks your calculation and lets you place the pirate and seagull masses at their locations to demonstrate the stability of the plank. If your calculation is correct the plank should balance as shown below in Fig-6. When you are ready hang the pirate and seagull at their positions on the meter stick. Carefully lower the supporting jack stand. Does it balance and the pirate survive? Yes Glug Note the jack is lowered and it is not supporting the plank. End of Lab 8 Please return the masses to the container on your table and put the meter stick and the hangars on the table . -------------------------- O