Question

A particle of mass $1kg$ slides down a frictionless track $\left(AOC\right)$ starting from rest at a point $A$ $\left(height2m\right)$. After reaching $C$, the particle continues to move freely in air as a projectile. When it reaches its highest point $P$$\left(height1m\right)$ the kinetic energy of the particle $\left(inJ\right)$ is:(Figure drawn is schematic and not to scale; take $g=10m{s}^{-2}$_____.

Answer 1

Step1: Given data.

Mass of the particle $m=1kg$

Height at point $\left(A\right)$, $h_A=2m$

Height at point $\left(P\right)$, $h_P=1m$

Step2: Finding the Final kinetic energy of the freely moving particle.

We know that,

From given figure mechanical energy conservation between point $A$ and $P$.

$U_i+K_i=U_f+K_f$

Where,

$U_i$ is initial potential energy

$U_f$ is final potential energy

$K_i$ is initial kinetic energy

$K_f$ is final kinetic energy

now,

$U_i+K_i=U_f+K_f$

$\Rightarrow$$mg{h}_A+0=mg{h}_P+K_f$

$\Rightarrow$ $K_f=mg{h}_A-mg{h}_P$

$\Rightarrow$ $K_f=mg\left(h_A-h_P\right)$

$\Rightarrow$ $K_f=1\times 10\times \left(2-1\right)$

$\Rightarrow$ $K_f=10J$

Hence, the kinetic energy of the particle is $10J$