doing a lab

Lab 07 – Force Vectors Purpose Students will quantify mechanical advantage for lateral rope tension. Theory A car is stuck in the mud on a road nobody uses. The driver has no phone, but has a strong, stiff rope. How can he pull his vehicle free of the mud hole? He ties one end of the rope to the frame of the car, and the other around a tree out front. The rope must be as tight as possible. He pulls sideways on the midpoint of the rope as hard as he can, and the car gets pulled forward an inch or so. He tightens the rope around the tree and repeats ‘til the car is free. Procedure 1. Fill a jar or bottle with a tight-fitting lid full of water and tighten the lid with a string or strong thread trapped in it so it can pull the container. The string must be at least a meter long. 2. Set the container on its side on the floor (preferably carpet so it is unlikely to roll sideways) and tie the other end of the string to a table leg, heavy chair leg, or something else near that floor that is hard to move. 3. Pull the container away from the anchor point so the string is tight. 4. Cut a rubber band so it is one long elastic cord and tie one end of it around the very middle of the string. This will be used to pull sideways on the string. 5. With a pen or marker, put two dots on the rubber band 5 cm apart. 6. Pull sideways via the free end of the rubber band until the container moves, and then keep the same tension on the rubber band while measuring how far apart the dots are now. This should be possible because the jar should seem to get harder to move as the path of the string becomes less straight. 7. Tip the container up, unscrew the lid to remove the string, and instead trap the end of the rubber band in it. 8. Set the container on its side again, and see how far apart the dots get if the rubber band is pulled hard enough to directly start to pull the container. Figure 07: Lateral tension moves a full water bottle slightly in this exaggerated drawing. Analysis Please answer each of the following in Canvas with complete sentences: 1. If a straight rope has a 0° bend in it, the mechanical advantage in a bent one for this lateral-tension trick comes out to 2/sin(θ/2). That is to say, applying just 10 lbs of force sideways with a 5° deflection in the rope pulls on the car with 10·2/sin(2.5) = 460 lbs. When the angle gets big, the advantage falls off massively. Stretchy ropes always ruin this car-pulling trick. Explain why. 2. Let the distances you measured in centimeters in parts 6 and 8 be ℓ and s, respectively. Mechanical advantage is then (s–5)/(ℓ–5). What is this value?

doing a lab

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