A car weighing 1400 kg is moving at a speed of 54 kmh^-1 up a hill when the motor stops. If it

step 1 In this question we have given that a car whose weight is 1 ,400 kilogram is moving at a speed o

A car weighing 1400 kg is moving at a speed of 54 kmh^-1 up...

A car weighing $1400 \mathrm{~kg}$ is moving at a speed of $54 \mathrm{kmh}^{-1}$ up a hill when the motor stops. If it is just able to reach the destination which is at a height of $10 \mathrm{~m}$ above the point, then the work done against friction (negative of the work done by the friction) is (Take $g=10 \mathrm{~ms}^{-2}$ ) (a) $10 \mathrm{~kJ}$ (b) $15 \mathrm{~kJ}$ (c) $17.5 \mathrm{~kJ}$ (d) $25 \mathrm{~kJ}$

A car weighing $1400 \mathrm{~kg}$ is moving at a speed of $54 \mathrm{kmh}^{-1}$ up a hill when the motor stops. If it is just able to reach the destination which is at a height of $10 \mathrm{~m}$ above the point, then the work done against friction (negative of the work done by the friction) is (Take $g=10 \mathrm{~ms}^{-2}$ )
(a) $10 \mathrm{~kJ}$
(b) $15 \mathrm{~kJ}$
(c) $17.5 \mathrm{~kJ}$
(d) $25 \mathrm{~kJ}$

Key Concepts

Conservation of Energy

This principle states that the total energy in a closed system remains constant, although it can transform from one type to another. In scenarios where friction is present, some of the mechanical energy is converted into thermal energy, meaning that the energy available for doing mechanical work (such as raising a mass against gravity) is less than the initial energy.

Kinetic Energy

Kinetic energy is the energy possessed by a body due to its motion and is calculated using the expression ½mv². It plays a crucial role in problems where moving objects are involved because it represents the initial energy that transitions into other forms, such as potential energy or energy dissipated by friction.

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field, given by the formula mgh. It is key in problems involving vertical displacement, as it quantifies the energy required to elevate a mass to a certain height against the force of gravity.

Work Done Against Friction

Work done against friction refers to the energy lost due to frictional forces as an object moves. It is calculated by determining the difference between the initial mechanical energy and the energy that is successfully converted into gravitational potential energy. This concept is central in analyzing situations where friction dissipates energy and affects the motion of objects.

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