What change in kinetic energy does an airplane experience on takeoff if it is moved a distance of 480m by a sustained net force of 5400N ?
Express your answer to two significant figures and include the appropriate units.
Student
To find the change in kinetic energy, we need to use the work-energy theorem. The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy.
The formula for work is given by:
Work (W) = Force (F) * Distance (d) * cosine(theta)
Where:
W = Work done
F = Force applied
d = Distance covered by the object
theta = Angle between the force and the direction of motion
In this case, the direction of motion is in the same direction as the force, so the angle (theta) between them is 0 degrees. Cosine(0) is equal to 1, so we can simplify the formula to:
Work (W) = Force (F) * Distance (d)
We can rearrange this equation to solve for the force:
Force (F) = Work (W) / Distance (d)
Now, let's plug in the given values:
Force (F) = 5400 N
Distance (d) = 480 m
Substituting these values into the equation:
Force (F) = 5400 N * 480 m = 2592000 N·m
Since work is the same as the change in kinetic energy, we can say:
Change in Kinetic Energy = Work = 2592000 N·m
To express the answer in appropriate units, we can convert the unit of work from N·m (Newton-meter) to Joules (J):
1 N·m = 1 J
Change in Kinetic Energy = 2592000 J
Therefore, the change in kinetic energy that the airplane experiences on takeoff is 2,600,000 Joules (J).