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High Plank

This high plank is an example of a 2nd class lever. The fulcrum is at the feet, the load is at the centre of gravity of the body, and the effort is at the hands.

If I know:

  • My weight (the load force).
  • The distance from my hands to my feet (the effort distance).
  • The distance from my centre of my gravity to my feet (the load distance).

How can I work out the effort force exerted by my hands on the floor? I am trying to calculate the mechanical advantage (MA = Load force/ Effort force) as well, but I need to know the effort force first.

Qmechanic
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Lisa
  • 17

2 Answers2

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For a general case, you will also need to know the angle your body makes with the ground, the angle your arms make with the ground, and the angle your feet make with the ground. Then, you can write down the force and torque equations for your body, with the force by your arms and the force by your feet as the unknowns. Solving these two equations will give you the two variables.

In this case, assuming your arms and feet are vertical, the directions of both forces is upwards, and thus the information you've given is sufficient. Solving the equations will give you: $F = \frac {mgd}{L}$ where $d$ is the load distance, and $L$ is the effort distance.

Deschele Schilder
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dnaik
  • 1,076
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Use the lever rule

fig

$$ \begin{aligned} F_A &= \frac{b}{a+b} W\\ F_B &= \frac{a}{a+b} W\\ \end{aligned}$$

What you are doing is balancing the torque about the center of mass, such that $a\, F_A = b\, F_B$.

John Alexiou
  • 38,341
  • See this answer for the concept of torque (or moment about a point). The equations are derived from the balance (shown above) and the fact that together they must add up to the weight $F_A + F_B = W$. Two equations + two unknowns = solution. – John Alexiou Aug 18 '20 at 23:41