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A particle m=...

Question

A particle $(m = 1 k g)$ slides down a frictionless track $(A O C)$ starting from rest at a point $A$ (height $2 m$ ).After reaching $C$ , the particle continues to move freely in air as a projectile. When it reaching its highest point $P$ (height $1 m$ ) ,the kinetic energy of the particle (in $J$ ) is Figure drawn is schematic and not to scale; take $g = 10 m / s^{2}$

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Solution

As the track $A O C$ is frictionless and the force field is gravitational is conservative so the energy along the whole motion will be conserved.Taking ground as datum where $P E = 0$

${(P E + K E)}_{A} = {(P E + K E)}_{p}$

$m g h_{a} + 0 = m g h_{p} + K E_{p}$

$(a s v = 0 a t A s o K E_{A})$

$K E_{p} = m g (h_{A} - h_{p})$

$= 1 \times 10 (2 - 1)$

$= 1 \times 10 \times 1$

$K E_{p} = 10 J$

Final Answer: $10$

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