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A metre stick, suspended from its mid-point, has a weight of 1.8 N hanging from the 20 cm mark - Junior Cycle Science - Question f - 2015

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A metre stick, suspended from its mid-point, has a weight of 1.8 N hanging from the 20 cm mark. Calculate where a student must hang a weight of 2.7 N so that the met... show full transcript

Worked Solution & Example Answer:A metre stick, suspended from its mid-point, has a weight of 1.8 N hanging from the 20 cm mark - Junior Cycle Science - Question f - 2015

Step 1

Calculate the moment due to the 1.8 N weight

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Answer

To find the moment caused by the 1.8 N weight, we use the formula:

extMoment=extforceimesextdistance ext{Moment} = ext{force} imes ext{distance}

Here, the force is 1.8 N and the distance from the pivot (the midpoint at 50 cm) is 50 - 20 = 30 cm. Therefore:

extMoment1.8N=1.8imes30=54extNm ext{Moment}_{1.8N} = 1.8 imes 30 = 54 ext{ Nm}

Step 2

Calculate the distance for the 2.7 N weight to balance

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Answer

For the stick to be balanced, the moment from the 2.7 N weight must equal the moment caused by the 1.8 N weight:

54=2.7imesextdistance54 = 2.7 imes ext{distance}

Rearranging gives:

ext{distance} = rac{54}{2.7} = 20 ext{ cm}

Step 3

Determine the position to hang the 2.7 N weight

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Answer

To find where to hang the 2.7 N weight, we need to add the distance calculated to the pivot point:

extPosition=50extcm+20extcm=70extcm ext{Position} = 50 ext{ cm} + 20 ext{ cm} = 70 ext{ cm}

Thus, the student must hang the weight at the 70 cm mark.

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