You are driving your 1500 kg car at 20 m / s down a hill with a 5.0^∘ slope when a deer suddenly

step 1 Here for the solution, use the law of conservation of energy to find the distance covered by the

You are driving your 1500 kg car at 20 m / s down a hill...

You are driving your $1500 \mathrm{kg}$ car at $20 \mathrm{m} / \mathrm{s}$ down a hill with a $5.0^{\circ}$ slope when a deer suddenly jumps out onto the roadway. You slam on your brakes, skidding to a stop. How far do you skid before stopping if the kinetic friction force between your tires and the road is $1.2 \times 10^{4} \mathrm{N}$ ? Solve this problem using conservation of energy.

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Key Concepts

Work Done by Friction

Friction is a nonconservative force that does work by converting mechanical energy (such as kinetic energy) into thermal energy, effectively removing energy from the system. The work done by friction is calculated as the friction force multiplied by the distance over which it acts, and it plays a critical role in stopping motion.

Conservation of Energy

This concept states that the total energy of a closed system remains constant, even though energy can be transformed from one type to another. In problems like this, energy is converted from kinetic energy to thermal energy via work done by nonconservative forces like friction.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. It is given by the expression (1/2)mv² in classical mechanics, and in braking scenarios, this energy must be dissipated in order to bring the object to a stop.

Dynamics on an Inclined Plane

When an object moves along an incline, gravitational forces have components both parallel and perpendicular to the surface. The parallel component (mg sin?) contributes to the acceleration or deceleration along the slope, influencing how much additional energy the friction must counteract when stopping.

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