A ski tow operates on a 15.0^∘ slope of length 300 m . The rope moves at 12.0 km / h and provide

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A ski tow operates on a 15.0^∘ slope of length 300 m . The...

A ski tow operates on a $15.0^{\circ}$ slope of length 300 $\mathrm{m} .$ The rope moves at 12.0 $\mathrm{km} / \mathrm{h}$ and provides power for 50 riders at one time, with an average mass per rider of 70.0 $\mathrm{kg} .$ Estimate the power required to operate the tow.

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Key Concepts

Gravitational Potential Energy

This concept involves the energy an object gains when it is raised to a higher elevation. In this type of problem, the change in gravitational potential energy (mgh) is used to estimate the work done in lifting the riders up the slope against gravity.

Power Calculation

Power is defined as the rate at which work is done or energy is transferred. In this scenario, the power required for the tow is determined by dividing the total work done (increasing gravitational potential energy of all riders) by the time taken to complete the lift.

Inclined Plane Mechanics

When dealing with inclined planes, it is necessary to account for the geometry of the slope. The vertical height reached is calculated using the sine of the slope angle multiplied by the length of the slope, which then factors into the gravitational potential energy calculations.

Unit Conversion

In many physical problems, the values provided need to be converted to proper SI units to ensure consistency in calculations. For instance, converting speeds from kilometers per hour to meters per second is crucial for accurately computing power.

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