A 18000kg airplane lands with a speed of 77 m/s on a stationary aircraft carrier deck that is 115 m long.
Find the work done by nonconservative forces in stopping the plane.
How do i do this?
To find the work done by nonconservative forces in stopping the plane, we need to determine the change in kinetic energy of the airplane as it slows down. The work done by nonconservative forces can be calculated using the work-energy theorem.
The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. Mathematically, it can be expressed as:
Net Work (W_net) = ΔKE
To calculate ΔKE, we need to find the initial and final kinetic energies of the airplane.
1. Find the initial kinetic energy (KE_initial):
The initial kinetic energy can be calculated using the formula:
KE_initial = (1/2) * mass * velocity^2
Here, the mass of the airplane is given as 18000 kg, and the initial velocity is given as 77 m/s. Plugging these values into the formula, we get:
KE_initial = (1/2) * 18000 kg * (77 m/s)^2
2. Find the final kinetic energy (KE_final):
As the airplane comes to a stop, its final velocity (VF) will be 0 m/s. Therefore, the final kinetic energy is:
KE_final = (1/2) * mass * velocity_final^2
In this case, velocity_final is 0 m/s, so the final kinetic energy simplifies to 0.
3. Calculate the change in kinetic energy (ΔKE):
The change in kinetic energy is the difference between the initial and final kinetic energies:
ΔKE = KE_final - KE_initial
Substituting the values, the term (KE_final - KE_initial) becomes (0 - KE_initial). So, effectively, ΔKE = -KE_initial.
Finally, the work done by nonconservative forces (W_net) is equal to the negative value of the initial kinetic energy:
W_net = -KE_initial
Therefore, we can now calculate the work done by nonconservative forces by substituting the values into the equation.
Note: In this case, the nonconservative forces include air resistance, friction, and other dissipative forces acting on the plane as it slows down.
I hope this explanation helps you understand how to solve the problem.
all of the KE the aircraft has is transfered to work done by fricton.
So calculate 1/2 m v^2