Question

A car of mass $500kg$ is at rest at point $X$ on a slope,as shown.
The car's brakes are released and the car rolls down the slope with its engine switched off. At point $Y$ the car has moved through a vertical height of $30m$ and has a speed of $11m{s}^{-1}$.
What is the energy dissipated by frictional forces when the car moves from $X$ to $Y$?

• A. $3.0\times {10}^{4}J$
• B. $1.2\times {10}^{5}J$
• C. $1.5\times {10}^{5}J$
• D. $1.8\times {10}^{5}J$

Answer 1

The correct option is B $1.2\times {10}^{5}J$

As the car rolls down the slope its gravitational potential energy is being converted to kinetic energy and work done against friction.

Loss in gravitational potential energy $=$ gain in Kinetic energy + work done against friction $mgh=\frac{1}{2}m{v}^2+$ work done against friction.

$\Rightarrow$ Work done against friction $=mgh-\frac{1}{2}m{v}^2$

Work done against friction $=(500\times 9.81\times 30)-(\frac{1}{2}\times 500\times {11}^2)$

Work done against friction $=1169005=1.2\times {10}^{5}J.$

Hence, the answer is $1.2\times {10}^{5}J.$