A model airplane of mass 0.7 kg is attached
to a horizontal string and flies in a horizontal
circle of radius 5.6 m, making 1.6 revolutions
every 7 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
Forget about the weight data. You would need the lift coefficient and wing area to get the velocity from the weight.
The plane travels 1.6*2*pi*5.6 meters in 7 s.
That is all you need to compute the speed.
To find the speed of the plane, we can use the formula for centripetal acceleration:
a = v^2 / r
where:
a is the centripetal acceleration,
v is the speed of the plane, and
r is the radius of the circular path.
In this case, the centripetal acceleration is provided by the force of gravity, so we can set the centripetal acceleration equal to the acceleration due to gravity:
a = 9.81 m/s^2
The radius of the circular path is given as 5.6 m.
Now, we can substitute these values into the formula and solve for v:
9.81 m/s^2 = v^2 / 5.6 m
To solve for v, we can rearrange the equation:
v^2 = 9.81 m/s^2 * 5.6 m
v^2 = 54.936 m^2/s^2
Taking the square root of both sides:
v ≈ √54.936 m^2/s^2
v ≈ 7.41 m/s
Therefore, the speed of the plane is approximately 7.41 m/s.
To find the speed of the plane, we can use the concept of centripetal acceleration. Centripetal acceleration is the acceleration of an object moving in a circular path and is directed towards the center of the circle.
We can calculate the centripetal acceleration using the following formula:
a = (v^2) / r
where:
a is the centripetal acceleration,
v is the velocity of the plane, and
r is the radius of the circular path.
In this case, we know the radius of the circular path, which is 5.6 m. However, we need to find the velocity of the plane.
To find the velocity, we need to determine the time it takes for the plane to complete one revolution. From the given information, we know that the plane makes 1.6 revolutions every 7 seconds. Therefore, the time for one revolution can be calculated as:
time for one revolution = 7 s / 1.6
Once we have the time for one revolution, we can calculate the velocity using the formula:
v = 2 * π * r / time for one revolution
where:
v is the velocity of the plane,
r is the radius of the circular path, and
time for one revolution is the time it takes for the plane to complete one revolution.
Now we have all the necessary values to calculate the speed of the plane.