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Potential Energy Formulae

A force shown...

Question

A force shown in the $F - x$ graph is applied to a $5 k g$ cart, which then climbs up a ramp as shown. The maximum height $Y_{m a x}$ the cart can reach (in $m$ ) is

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Solution

We have,
$Δ$ KE = Work done
= Area under $F - x$ graph
$= \frac{1}{2} \times 4 \times 50 = 100 J$
This gets converted into Potential Energy as the block climbs the ramp.
$m g Y_{max} = 100 50 Y_{max} = 100 \Rightarrow Y_{max} = 2 m$

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