Question

H wishes to move a rock by using an 8-foot steel bar placed on a fulcrum 18 inches from the rock, How much force must she apply on the long end to lift the rock which weighs 858 pounds?

Answer 1

`198^("lb")`

Explanation:

There is a slight problem with this question. The bar will be at an angle to the horizontal ground. Consequentially the horizontal distances between fulcrum, load and applied force will change as the angle to the horizontal changes.

`color(brown)("This condition is ignored in the presented solution.")`

Did you know you can manipulate units of measurements the same way you do the numbers?

Let work done be`" force "xx" distance"`

Clockwise moments cancel out anticlockwise moment

The moment of the load to the fulcrum is

`858^("lb")xx18" inches "=15444" inch pounds"`

The moment of the applied force is

`F^("lb")xx78" inches "= 78F" inch pounds"`

Thus for all forces to equalise we have:

`78F" inch pounds"=15444" inch pounds"`

`F^("lb")=15444/78 (cancel("inch")" pounds")/(cancel("inches"))= 198" pounds"`

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Technically applying just 198 pounds puts the system in equilibrium and nothing moves. You would need to apply a bit more than 198 lb to have movement. Once lifted and stationary you would then be applying the 198 lb