Question

A car weighing $1400kg$ is moving at a speed of $54km/hr$ up hill when the motor stops. If it is just able to reach the destination which is at a height of $10m$ above the point calculate the work done against friction (negative of the work done by the friction).

Answer 1

Car Mass $m=1400kg$ .

$h=10m$

Moving at Initial speed $v=54km/h=15m/sec.$

Now Initial Kinetic Energy of the car ,

$=\frac{1}{2}m{v}^2$

$=\frac{1}{2}\times (1400\times {15}^2)$

$=157500J$.

Here final velocity and Final Kinetic energy both are Zero.

Now change in Kinetic Energy

= Final - Initial

$=0-157500$

$=-157500J.$

So change in Kinetic energy is also equal to Work done by all force.

Thus work done by gravity,

$=mgh$

$=1400\times 9.8(-10)$

$=1400\times -98$

$=-137200$ .

Here, change in Kinetic energy = Work done by the friction + Work done by the gravity.

$-157500=$ Work done by friction $+(-137200)$

Work done by the friction $=-157500+137200$

$=-20,300$

Hence, the work done against the friction $=20300J$