A 60.0 kg skier starts from rest at the top of a ski slope 63.0 m high. (a) If friction forces

step 1 Hi, here in this given problem, mass of the scare that is given as m is equal to 60 .0 kilogram

A 60.0 kg skier starts from rest at the top of a ski slope...

A $60.0 \mathrm{~kg}$ skier starts from rest at the top of a ski slope $63.0 \mathrm{~m}$ high. (a) If friction forces do $-10.9 \mathrm{~kJ}$ of work on her as she descends, how fast is she going at the bottom of the slope? (b) Now moving horizontally, the skier crosses a patch of soft snow where $\mu_{\mathrm{k}}=0.21$. If the patch is $65.0 \mathrm{~m}$ wide and the average force of air resistance on the skier is $180 \mathrm{~N}$, how fast is she going after crossing the patch? (c) The skier hits a snowdrift and penetrates $3.0 \mathrm{~m}$ into it before coming to a stop. What is the average force exerted on her by the snowdrift as it stops her?

A $60.0 \mathrm{~kg}$ skier starts from rest at the top of a ski slope $63.0 \mathrm{~m}$ high. (a) If friction forces do $-10.9 \mathrm{~kJ}$ of work on her as she descends, how fast is she going at the bottom of the slope? (b) Now moving horizontally, the skier crosses a patch of soft snow where $\mu_{\mathrm{k}}=0.21$. If the patch is $65.0 \mathrm{~m}$ wide and the average force of air resistance on the skier is $180 \mathrm{~N}$, how fast is she going after crossing the patch?
(c) The skier hits a snowdrift and penetrates $3.0 \mathrm{~m}$ into it before coming to a stop. What is the average force exerted on her by the snowdrift as it stops her?

Key Concepts

Energy Conservation

Energy conservation involves the principle that energy can neither be created nor destroyed, only transformed from one form to another. In problems like this, potential energy is converted into kinetic energy as an object falls, but non-conservative forces like friction can remove energy from the system by converting it to thermal energy.

Work-Energy Theorem

The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. This concept is crucial when accounting for various forces doing work, such as friction and air resistance, which either add to or subtract from the system's energy.

Gravitational Potential Energy

Gravitational potential energy is the energy stored in an object due to its height above a reference point. It is calculated as the product of mass, gravitational acceleration, and height (mgh) and is the initial reservoir of energy that, when converted, affects the object's speed at lower elevations.

Kinetic Energy

Kinetic energy is the energy of motion, given by the formula (1/2)mv². It represents the amount of work needed to accelerate an object from rest to a certain velocity and is the energy that the skier gains as she descends the slope.

Friction and Non-Conservative Work

Friction and other non-conservative forces, such as air resistance, perform work that depends on the path taken and usually results in the dissipation of mechanical energy as heat. Their negative work subtracts from the mechanical energy available for conversion into kinetic energy, thus reducing the final velocity of the object.

Force-Work Relationship

The relationship between force and work is encapsulated in the equation work = force × distance × cos(theta), where theta is the angle between the force and the displacement vector. This concept is used to determine quantities like stopping force, where the work done by a force over a distance equals the change in the object's kinetic energy.

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