Mechanical Advantage - k-12
You need to push a 500 kg grand piano onto a stage that is 3 m above the ground. If you can only apply a maximum force of 1000 N, what is the minimum distance from the stage that you should begin building your ramp?
2 Answers
To solve this question, you need to understand the concept of mechanical advantage (MA). Mechanical advantage refers to a scenario where you put into a smaller force and get a greater force output. The compensation for that, however, is that you will need to exert the force for a longer distance.
MA = d_input / d_output = F_output / F_input
By rearranging the above we have: d_input = F_output / F_input * d_output = 500 * 10 / 1000 * 3 = 15 m.
So we need to longest side of the ramp would 15 m. So the distance from the stage = sqrt(15^2 - 3^2) = 14.7 m (3 significant figures)
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This question can be solved by considering energy conservation as below:
To lift Piano of 500 kg by 3 mtr, we require 500x10x3 Joule energy
This energy can be obtained by doing work done on Piano by pushing with force 1000 N upto 's' mtr (assume). Work done = 1000s joule
By equating, s=15 mtr
Now Ramp is a 90 degree triangle with height 3 mtr, hypoteneous=s mtr = 15 mtr, and base (minimum distance from the stage)=b,
hence, b= square root of (square of 15-square of 3) = 14.7 mtr
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