Why does a car require more fuel to climb a hill?

A car requires more fuel to climb a hill due to the increased work against gravitational force.

When a car is moving on a flat surface, the engine's primary job is to overcome friction and air resistance. However, when the car starts to climb a hill, the engine must also work against the force of gravity. This additional work requires more energy, which in turn requires more fuel.

The force of gravity acting on the car is given by the equation F = m*g, where m is the mass of the car and g is the acceleration due to gravity. When the car is on a flat surface, this force is balanced by the normal force from the ground, so it doesn't affect the car's motion. However, when the car is climbing a hill, the force of gravity is acting downwards and backwards, opposing the car's motion. This means the engine must exert an additional force to overcome gravity and keep the car moving upwards.

The work done by the engine to move the car up the hill is given by the equation W = F*d, where F is the force required and d is the distance travelled. The force required is the sum of the force to overcome friction and air resistance, and the force to overcome gravity. As the angle of the hill increases, the component of the gravitational force acting against the car's motion also increases, so the total force required, and therefore the work done by the engine, also increases.

This additional work requires additional energy, which comes from burning more fuel. The efficiency of the engine also plays a role here. No engine is 100% efficient, so some of the energy from the fuel is always lost as heat. This means that the engine must burn even more fuel to provide the necessary energy to climb the hill.

In summary, a car requires more fuel to climb a hill because the engine must do more work to overcome the additional force of gravity acting against the car's motion. This additional work requires more energy, which comes from burning more fuel.