A model airplane of mass 0.9 kg is attached
to a horizontal string and flies in a horizontal circle of radius 5.2 m, making 1.2 revolutions
every 8 s. (The weight of the plane is balanced
by the upward “lift” force of the air on the
wings of the plane.)
The accelaration due to the gravity is 9.81
m/s2.
Find the speed of the plane
see below
To find the speed of the plane, we can use the concept of centripetal acceleration. Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It is given by the formula:
a = (v² / r)
where:
a is the centripetal acceleration,
v is the velocity (speed) of the object,
and r is the radius of the circular path.
In this case, since the plane is moving in a circle of radius 5.2 m, we need to find its velocity (speed) to calculate the centripetal acceleration.
To find the velocity, we can use the formula:
v = (2 * π * r) / T
where:
v is the velocity (speed) of the object,
π is pi (approximately 3.14159),
r is the radius of the circular path,
and T is the time taken to complete one revolution.
In this case, the plane makes 1.2 revolutions every 8 seconds, so T = 8 s / 1.2 = 6.67 s.
Now, we can substitute the values into the equation to find the velocity:
v = (2 * π * 5.2) / 6.67
Calculating this equation gives us:
v ≈ 3.88 m/s
Therefore, the speed of the plane is approximately 3.88 m/s.