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Mechanical Advantage

Machines allow us to do large amounts of work while exerting less force.

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A Daily Advantage

What are some common sources of mechanical advantage in our daily lives?


Credit: mateoutah
Source: http://www.flickr.com/photos/matthewblank/133440530/sizes/o/in/photolist-cMVdN-nnHik-um1Md-wzZuq-ENF1u-HEjvA-HEkGW-HEpgk-HEqqc-Kcm3f-2ygKdf-2FbRCF-2Na2BE-3oy7SS-4vu2YQ-4X1VJY-5oJFzM-5BTduc-62ruhG-6fvfLy-6iV6xM-6CatjE-6F1J9v-6YHtRC-6ZSggf-72oLMV-72oMAa-7no45z-7oZFT1-7u93iD-aYErut-9yx6Ms-9N8JDk-9tZz9A-9Ahpnm-9whMtH-8GXXXY-daicTX-daziTL-ey78dZ-abFZas-9N8JDt-9Y2ari-bfAGn4-cs2Dwj-9daCvf-cs2DAC-8AcGzG-9W1jdZ-cgfWuE-8UaU6T/
License: CC BY-NC 3.0

Whether or not you realize it, you utilize mechanical advantage on a daily basis. Maybe the lid of a pickle jar is tightly shut, so you use a flat-edged screwdriver as a lever to pry it open. Maybe one of your grandparents uses a wheelchair, so instead of taking the stairs up to the shopping center, you wheel him or her up the wheelchair ramp.

Mechanical advantage means putting a smaller force into a simple machine to output a larger one. It certainly makes our lives easier, but it actually gives us a little less extra output than we would expect. This is because factors such as friction and machine wear over time cause a loss of energy. Actual mechanical advantage takes these factors into account, while ideal mechanical advantage does not. 

Creative Applications

  1. You want to build a wheelchair ramp at the front of your home for your grandfather. The maximum safe force you can exert on his wheelchair is 100 N, and he weighs 70 kg. The ramp will be a meter tall. How long should it be at minimum? (Hint: use the formulas \begin{align*}MA = \frac{F_{out}}{F_{in}}\end{align*}MA=FoutFin and \begin{align*}MA = \frac{d_{in}}{d_{out}}\end{align*}MA=dindout.)
  2. Efficiency is the ratio of actual to ideal mechanical advantage. It measures how well a machine works. Do you think there is such thing as a fully-efficient (100%) machine? Explain.
  3. Aside from the simple machines mentioned in the text, what are some other common ones?


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