A sustained force of 44 N moves a model airplane 10 m along its runway to provide the required speed for takeoff. Find the kinetic energy at takeoff.
To find the kinetic energy at takeoff, we can use the formula for kinetic energy:
Kinetic Energy (KE) = 0.5 * mass * velocity^2
Since we are given the force (44 N) instead of mass, we need to find the mass of the model airplane first. We can do this using Newton's second law:
Force = mass * acceleration
The acceleration (a) can be calculated using Newton's second law:
a = Force / mass
Rearranging the formula, we can solve for mass:
mass = Force / acceleration
To find the acceleration, we can use one of Newton's three laws of motion:
F = m * a
Rearranging the formula, we find:
a = F / m
Now we can combine the above two equations to solve for mass:
mass = Force / (F / m)
By simplifying, we get:
mass = m
Now, substituting the given values:
mass = 44 N / (F / m)
Simplifying further:
mass = 44 N * (m / F)
mass = 44 m / F
Now that we have the mass, we can calculate the acceleration:
acceleration = Force / mass
acceleration = 44 N / mass
Substituting the given values:
acceleration = 44 N / (44 m / F)
Simplifying:
acceleration = F / m
Finally, we can calculate the velocity using the equation of motion:
velocity = initial velocity + acceleration * time
Since the airplane starts from rest, the initial velocity is zero:
velocity = acceleration * time
Since the airplane covers a distance of 10 m, we can calculate the time taken using:
velocity = distance / time
Rearranging the formula, we get:
time = distance / velocity
time = 10 m / velocity
Now we can substitute the calculated value of velocity back into the equation for time.
Once we have the velocity, we can substitute it into the formula for kinetic energy:
Kinetic Energy (KE) = 0.5 * mass * velocity^2
Now plug in the calculated values of mass and velocity into the formula, and solve for the kinetic energy at takeoff.