A plane designed for vertical takeoff has a mass of 8.2 ✕ 103 kg. Find the net work done by all forces on the plane as it accelerates upward at 10.5 m/s2 through a distance of 25.4 m after starting from rest.

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To find the net work done on the plane, we can use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.

To find the work done by all forces on the plane, we need to calculate the change in its kinetic energy. The formula for kinetic energy is given by:

Kinetic Energy (KE) = (1/2) * mass * velocity^2

Initially, the plane is at rest, so its initial kinetic energy is zero. The final kinetic energy can be calculated using the final velocity. We can find the final velocity using the kinematic equation:

Final velocity (v) = initial velocity + (acceleration * time)

Since the plane is accelerating upward at 10.5 m/s^2, we can assume that the initial velocity is 0.

Using the given distance of 25.4 m, we can calculate the time taken during the acceleration using the kinematic equation:

Distance (d) = (1/2) * acceleration * time^2

Solving for time (t):

25.4 = (1/2) * 10.5 * t^2

t^2 = 25.4 / (0.5 * 10.5)
t^2 = 4.838
t ≈ 2.20s

Substituting the values into the equation for final velocity:

Final velocity (v) = 0 + (10.5 * 2.20)
v ≈ 23.1 m/s

Now, we can calculate the final kinetic energy (KE) using the formula:

KE = (1/2) * mass * velocity^2

KE = (0.5) * (8.2 * 10^3 kg) * (23.1 m/s)^2
KE ≈ 2.04 x 10^6 J

Since the initial kinetic energy is zero, the net work done by all forces on the plane is equal to the change in kinetic energy:

Net Work = KE - Initial KE
Net Work = 2.04 x 10^6 J - 0
Net Work ≈ 2.04 x 10^6 J

Therefore, the net work done by all forces on the plane as it accelerates upward is approximately 2.04 x 10^6 Joules.