The model airplane in Figure 5.6 is flying at a speed of 22 m / s on a horizontal circle of radi

step 1 So when we have our plane flying at a speed of V, and if the radius is R, then the force in the

The model airplane in Figure 5.6 is flying at a speed of 22...

The model airplane in Figure 5.6 is flying at a speed of $22 \mathrm{m} / \mathrm{s}$ on a horizontal circle of radius $16 \mathrm{m}$. The mass of the plane is $0.90 \mathrm{kg}$. The person holding the guideline pulls it in until the radius becomes $14 \mathrm{m}$. The plane speeds up, and the tension in the guideline becomes four times greater. What is the net work done on the plane?

Key Concepts

Work-Energy Principle

This principle states that the net work done on an object is equal to the change in its kinetic energy. It is used to relate forces doing work on a body to the increase or decrease in its motion energy, irrespective of the path taken by the object.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. In problems involving circular motion and changes in speed, the calculation of kinetic energy directly helps in determining how the work done on the object translates into changes in its speed.

Uniform Circular Motion

Uniform circular motion describes the motion of an object traveling at a constant speed along a circular path. It involves forces that act perpendicular to the object's velocity, such as centripetal force, which are essential when analyzing the dynamics of objects moving in a circle.

Centripetal Force

Centripetal force is the net force directed towards the center of the circle that keeps an object in circular motion. Understanding this concept is crucial in scenarios where the radius of the motion changes, as adjustments in the centripetal force affect the speed and tension in the system.

Conservation of Angular Momentum

This concept holds that in the absence of an external torque, the angular momentum of a system remains constant. In a situation where the radius of rotation changes, the conservation of angular momentum explains how the object's speed must adjust, which in turn impacts the kinetic energy and the work done on it.

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