A fighter jet is launched from an aircraft carrier with the aid of its own engines and a steam-powered catapult. The thrust of its engines is 2.3 x 10^5 N. In being launched from rest it moves a distance of 87 m and has a kinetic energy of 4.5 x 10^7 J at lift-off. What is the work done on the jet by the catapult?

To find the work done on the jet by the catapult, we first need to understand the concept of work and energy. Work done on an object is equal to the change in kinetic energy of the object. This relationship is derived from the work-energy theorem, which states that the work done by the net force acting on an object is equal to the change in its kinetic energy.

The work done by both the engines and the catapult is the change in kinetic energy which is given by:

Work_total = ΔKE = KE_final - KE_initial

Since the jet starts from rest, its initial kinetic energy (KE_initial) is 0. Therefore, we can write:

Work_total = KE_final

Given KE_final = 4.5 x 10^7 J, we already have the total work done on the jet. This total work is the sum of the work done by the jet's engines (Work_engines) and the work done by the catapult (Work_catapult). We can represent it as:

Work_total = Work_engines + Work_catapult

We know the force applied by the engines (F_engines = 2.3 x 10^5 N) and the distance over which this force is applied (d = 87 m). The work done by the engines can be calculated using the definition of work, which is the product of force and distance:

Work_engines = F_engines * d Work_engines = 2.3 x 10^5 N * 87 m Work_engines = 2.001 x 10^7 J

Now we can solve for the work done by the catapult (Work_catapult) by rearranging the previous equation:

Work_catapult = Work_total - Work_engines Work_catapult = 4.5 x 10^7 J - 2.001 x 10^7 J Work_catapult ≈ 2.499 x 10^7 J

Therefore, the work done on the jet by the catapult is approximately 2.499 x 10^7 joules.

Extra: Work and energy are fundamental concepts in physics. Work is defined as the process of energy transfer to or from an object via the application of force along a displacement. If an object is displaced by a force, we say that the force has done work on the object. The unit of work in the International System of Units (SI) is the joule (J).

In the context of the fighter jet being launched, the total energy required to accelerate the jet is provided by both the jet's engines and the catapult system together. Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 1/2 mv^2, where m is mass and v is velocity.

The work-energy theorem connects the concepts of work and kinetic energy, showing how forces acting on an object can change its kinetic energy, which is essentially its speed and, by extension, its ability to do things like climbing heights or carrying payloads. Understanding how the catapult contributes to the jet's overall launch is an application of these principles, which are fundamental in various areas of science and engineering.