A 1500 kg car begins sliding down a 5.0^∘ inclined road with a speed of 30 km / h. The engine

step 1 Well, mass of the car, M is equal to 1 ,500 kilograms. This is mass of the car. And theta is equ

A 1500 kg car begins sliding down a 5.0^∘ inclined road...

A $1500 \mathrm{~kg}$ car begins sliding down a $5.0^{\circ}$ inclined road with a speed of $30 \mathrm{~km} / \mathrm{h}$. The engine is turned off, and the only forces acting on the car are a net frictional force from the road and the gravitational force. After the car has traveled $50 \mathrm{~m}$ along the road, its speed is $40 \mathrm{~km} / \mathrm{h}$. (a) How much is the mechanical energy of the car reduced because of the net frictional force? (b) What is the magnitude of that net frictional force?

Key Concepts

Unit Conversion

Unit conversion is the process of converting measurements from one unit to another, such as converting speeds from kilometers per hour to meters per second. Ensuring consistency of units is vital for accurate calculations in physics problems.

Inclined Plane Analysis

Inclined plane analysis involves decomposing gravitational forces into components parallel and perpendicular to the plane’s surface. This method is crucial for problems involving slopes, as it helps determine the effective forces causing acceleration along the incline.

Frictional Work

Frictional work refers to the work done by friction forces, which generally opposes motion and reduces the mechanical energy of a system by converting it into thermal energy. Understanding this concept is essential when calculating energy losses in systems where friction is present.

Gravitational Potential Energy

Gravitational potential energy is the energy stored in an object due to its position in a gravitational field, typically expressed as the product of mass, gravitational acceleration, and height. This concept is critical when dealing with systems moving along inclines where vertical displacement plays a role.

Kinetic Energy

Kinetic energy is the energy that an object possesses due to its motion, calculated as one-half of the mass multiplied by the square of its velocity. It is a key component in analyzing changes in the energy of a system as an object accelerates or decelerates.

Work-Energy Principle

The work-energy principle states that the net work done on an object by all forces equals the change in its mechanical energy (the sum of kinetic and potential energy). This concept is fundamental for analyzing energy losses or gains due to non-conservative forces such as friction.

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