A model train with a mass of $8 kg$ is moving along a track at $9 (cm)/s$ . If the curvature of the track changes from a radius of $27 cm$ to $81 cm$ , by how much must the centripetal force applied by the tracks change?

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Answer 1 · 2016-05-22T02:13:53

Change in centripetal force $DeltaF=-16000" "$ Dynes

From $F=(mv^2)/r$

Solve for $DeltaF$

Replace $F$ with $F+DeltaF$ and $r$ with $r+Deltar$

$F=(mv^2)/r$
$F+DeltaF=(mv^2)/(r+Deltar)$

Subtract $F$ from both sides

$F+DeltaF-F=(mv^2)/(r+Deltar)-(mv^2)/r$

$cancelF+DeltaF-cancelF=(mv^2)/(r+Deltar)-(mv^2)/r$

$DeltaF=(mv^2)/(r+Deltar)-(mv^2)/r$

$DeltaF=(mv^2)(1/(r+Deltar)-1/r)$

But $Deltar=81-27=54$

$DeltaF=(8000(9)^2)(1/(27+54)-1/27)$

$DeltaF=-16000" "$ Dynes

God bless....I hope the explanation is useful.

A model train with a mass of 8 kg8 kg is moving along a track at 9 (cm)/s9 (cm)/s. If the curvature of the track changes from a radius of 27 cm27 cm to 81 cm81 cm, by how much must the centripetal force applied by the tracks change?