# Work and Energy

## Concept Of Physics

### H C Verma

1   The mass of cyclist together with the bike is $90$ kg. Calculate the increase in kinetic energy if the speed increases from $6'0$ km/h to $12$ km/h.

##### Solution :

$M$ = $m_c$ + $m_b$ = $90kg$ $\\$ $u$ = $6 km/h$ = $1.666 m/sec$ $\\$ $v$ = $12 km/h$ = $3.333$ m/sec $\\$ $increase$ in $K.E.$ = $\frac{1}{2}$ $Mv^2$ - $\frac{1}{2}$ $Mu^2$ $\\$ = $\frac{1}{2}$ $90$ $\times$ $(3.333)^2$ - $\frac{1}{2}$ $\times$ $90$ $\times$ $(1.66)^2$ = $494.5$ - $124.6$ = $374.8$ $\approx$ $375J$

$increase$ in $K.E.$ = $\frac{1}{2}$ $Mv^2$

2   A block of mass $2.00$ kg moving at a speed of $10.0$ m/s accelerates at $3.00$ m/s for $5.00$ s. Compute its final kinetic energy.

##### Solution :

$m_b$ = $2kg$ $\\$ $u$ = $10 m/sec$ $\\$ $a$ = $3 m/aec^2$ $\\$ $t$ = $5 sec$ $\\$ $v$ = $u$ + $at$ = $10$ + $3 I 5$ = $25 m/sec$ $\\$ $\therefore$ $F.K.E$ = $\frac{1}{2}$ $mv^2$ = $\frac{1}{2}$ $\times$ $2$ $\times$ $625$ = $625 J$

3   A box is pushed through $4.0$ m across a floor offering $100$ N resistance. How much work is done by the resisting force ?

##### Solution :

$F$ = $100 N$ $\\$ $S$ = $4m,$ $\theta$ = $0^o$ $\\$ $\omega$ = $F.S$ = $100$ $\times$ $4$ = $400$ $J$

4   A block of mass $5.0$ kg slides down an incline of inclination $30°$ and length $10$ m. Find the work done by the force of gravity.

##### Solution :

$m$ = $5kg$ $\\$ $\theta$ = $30^o$ $\\$ $S$ = $10$ $m$ $F$ = $mg$ $\\$ $So$ $work$ $done$ $by$ $the$ $force$ $of$ $gravity$ $\\$ $\omega$ = $mgh$ = $5$ $\times$ $9.8$ $\times$ $5$ = $245$ $J$

5   A constant force of $2.50$ N accelerates a stationary particle of mass $15$ g through a displacement of $2.50$ m. Find the work done and the average power delivered.