An automobile with passengers has weight 16400 N and is moving at 113 km / h when the driver b

step 1 So we know here that the weight is equaling 16 ,400 newtons. And so the mass would simply be equ

An automobile with passengers has weight 16400 N and is...

An automobile with passengers has weight $16400 \mathrm{~N}$ and is moving at $113 \mathrm{~km} / \mathrm{h}$ when the driver brakes, sliding to a stop. The frictional force on the wheels from the road has a magnitude of $8230 \mathrm{~N}$. Find the stopping distance.

Key Concepts

Work-Energy Principle

This principle states that the work done by the forces acting on an object is equal to the change in its kinetic energy. In problems involving stopping distances, the work done by friction (which is a non-conservative force) reduces the vehicle's kinetic energy to zero. The principle provides a powerful tool for analyzing situations where forces do work over a distance, leading to energy transformations.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion and is given by the formula ½ mv², where m is the mass and v is the velocity. In stopping distance problems, the initial kinetic energy of the vehicle is entirely dissipated by the work done against friction, making it a central concept in determining the stopping distance.

Friction

Friction is the resistive force that opposes motion between two surfaces in contact. In dynamics, friction is often modeled as a constant force during sliding motion. In this context, it is the force that does negative work on the vehicle during braking, converting the vehicle’s kinetic energy into thermal energy, and thereby bringing the vehicle to a stop.

Unit Conversion

Unit conversion is important to ensure consistency when applying physical formulas. For instance, converting speed from kilometers per hour to meters per second allows the kinetic energy calculation and work done by friction to be computed using standard SI units. This step is critical for accurate problem-solving in physics.

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