An airplane is flying in a horizontal circle at a
speed of 104 m/s. The 84.0 kg pilot does not
want the centripetal acceleration to exceed
6.98 times free-fall acceleration.
Find the minimum radius of the plane’s
path. The acceleration due to gravity is 9.81
m/s2
.
Answer in units of m
At this radius, what is the magnitude of the
net force that maintains circular motion exerted on the pilot by the seat belts, the friction
against the seat, and so forth?
Answer in units of N.
To elaborate further on Bobpursley's answer,
Acceleration outward at rim is, A = rω² = V²/r. V is the tangental velocity in m/s.
r is radius of circle in meters. ω is the angular velocity in radians/sec
a is in m/s².. so,
a = V²/r = (6.56)(9.81)
r = (104)² / (6.56)(9.81) = 168 m
Centripetal force is..
f = mV²/r = mrω²
ω is angular velocity in radians/sec
1 radian/sec = 9.55 rev/min
m is mass in Kilograms, R is radius of circle in meters, V is the tangental velocity in m/s, and Force (F) is in Newtons.
F = mV²/r = (82)(104)² / (168) newtons!
Maybe I'm overthinking it but, Heres my two cents.
Khan Academy also has videos on these :) Hope this helped!!
Why did the airplane start dating the runway?
Because it found out the runway had a lot of baggage!
Now, let's calculate the minimum radius of the plane's path. We know that the centripetal acceleration is given by the formula:
ac = v^2 / r
where ac is the centripetal acceleration, v is the speed, and r is the radius. The pilot does not want the centripetal acceleration to exceed 6.98 times the acceleration due to gravity. So, we have:
6.98 * 9.81 m/s^2 = (104 m/s)^2 / r
Now let's solve for r:
r = (104 m/s)^2 / (6.98 * 9.81 m/s^2)
r ≈ 170.20 m
So, the minimum radius of the plane's path is approximately 170.20 m.
Now, for the magnitude of the net force maintaining circular motion on the pilot, we can use the formula:
Fc = m * ac
where Fc is the net force, m is the mass of the pilot, and ac is the centripetal acceleration. Plugging in the values:
Fc = 84.0 kg * (104 m/s)^2 / 170.20 m
Fc ≈ 5127.86 N
Therefore, the magnitude of the net force maintaining circular motion on the pilot is approximately 5127.86 N.
To find the minimum radius of the plane's path, we need to start by finding the maximum allowable centripetal acceleration.
Given:
Speed (v) = 104 m/s
Mass of the pilot (m) = 84.0 kg
Free-fall acceleration (g) = 9.81 m/s^2
Centripetal acceleration (a) = 6.98 * g
The centripetal acceleration is given by the formula:
a = v^2 / r
Rearranging the formula, we can solve for the radius (r):
r = v^2 / a
Substituting the given values:
r = (104 m/s)^2 / (6.98 * 9.81 m/s^2)
Solving this equation will give us the minimum radius of the plane's path.
Now, let's calculate the minimum radius:
r = (104 * 104) / (6.98 * 9.81)
r = 1102.581 m
Therefore, the minimum radius of the plane's path is approximately 1102.581 m.
To find the magnitude of the net force exerted on the pilot by the seat belts, friction against the seat, etc., we need to calculate the centripetal force.
The centripetal force (F) is given by the formula:
F = m * a
Substituting the given values:
F = 84.0 kg * (6.98 * 9.81 m/s^2)
Now, let's calculate the magnitude of the net force:
F = 84.0 kg * 68.4318 m/s^2
F = 5754.7152 N
Therefore, the magnitude of the net force that maintains circular motion exerted on the pilot by the seat belts, friction against the seat, and so forth, is approximately 5754.7152 N.
To find the minimum radius of the plane's path, we need to use the formula for centripetal acceleration:
a = v² / r
where:
a = centripetal acceleration
v = velocity
r = radius
The given condition states that the centripetal acceleration should not exceed 6.98 times the acceleration due to gravity, which is:
a <= 6.98 * g
Plugging the given values into the equation, we get:
a = (104 m/s)² / r
6.98 * g = 6.98 * (9.81 m/s²)
Setting these two expressions for acceleration equal to each other and solving for r, we have:
(104 m/s)² / r = 6.98 * (9.81 m/s²)
To find r, we rearrange the equation:
r = (104 m/s)² / (6.98 * 9.81 m/s²)
Now we can calculate the minimum radius by plugging in the values:
r = (104 m/s)² / (6.98 * 9.81 m/s²)
r ≈ 161.63 m
Therefore, the minimum radius of the plane's path is approximately 161.63 m.
To find the magnitude of the net force exerted on the pilot, we can use the following equation:
F = m * a
where:
F = force
m = mass
a = acceleration
Since the only force acting on the pilot is the net force maintaining circular motion, we can substitute the centripetal acceleration into the equation:
F = m * (104 m/s)² / r
Plugging in the given values:
F = (84.0 kg) * (104 m/s)² / 161.63 m
Now we can calculate the magnitude of the net force by evaluating the expression:
F ≈ 5383.71 N
Therefore, the magnitude of the net force exerted on the pilot by the seat belts, friction against the seat, and other forces is approximately 5383.71 N.
acceleration=v^2/r or r=v^2/a
force= a*massOfPilot