Some gliders are launched from the ground by means of a...

Some gliders are launched from the ground by means of a winch, which rapidly reels in a towing cable attached to the glider. What average power must the winch supply in order to accelerate a 184 -kg ultralight glider from rest to $26.0 \mathrm{m} / \mathrm{s}$ over a horizontal distance of $48.0 \mathrm{m} ?$ Assume that friction and air resistance are negligible, and that the tension in the winch cable is constant.

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Key Concepts

Force under Constant Tension

When a constant force is applied—as in the case of a winch delivering a uniform pull via a constant-tension cable—the work done is simply the product of this constant force and the displacement. This simplification is crucial when linking the mechanical work performed to changes in the kinetic energy of an object.

Kinematics under Constant Acceleration

Kinematics deals with the motion of objects and, under the assumption of constant acceleration, allows us to relate displacement, time, velocity, and acceleration through its equations. These relationships are used to determine quantities like the time taken to cover a given distance while accelerating, which then connects to the calculation of power.

Work-Energy Principle

This principle states that the net work done on an object is equal to its change in kinetic energy. In problems where an object accelerates from rest, the work performed by the force is used to increase the object's kinetic energy, calculated as one-half of the mass times the square of its final velocity.

Average Power

Average power is defined as the rate at which work is performed, meaning it is the total work done divided by the total time over which the work is done. This concept is essential in understanding how quickly energy is transferred or converted within a system.

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