00:01
In this exercise, we're going to be talking about circular motion, so i'm going to briefly review the concept.
00:05
Consider that we have a particle that's undergoing circular motion, as shown in the picture, and we can decompose the particle's acceleration into two components.
00:14
One of them is d -sentrupital acceleration ac, and the other one is a tangential acceleration at.
00:22
De -sintripetal acceleration accounts for the change in direction of the velocity and is equal in magnitude 2v squared divided by r, and it points towards the center of the trajectory, while the tangential acceleration accounts for the change in speed and is equal to dvdt.
00:40
What we have in the exercise is an airplane that's traveling with a speed v of 50 meters per second, and the airplane is tilted, as shown in the picture, by an angle theta of 15 degrees.
00:55
And we have a pilot who only fuels the force of the the normal force that the seat exerts on him.
01:05
And the pilot has a mass of 70 kilograms.
01:10
Okay, now our goal is to find both the radius of curvature row and the normal force of the seed exerts on the pilot.
01:21
So what i'm going to do is to draw a force diagram.
01:25
So consider that this here is the pilot, okay, i'm just gonna represent it by this rectangle.
01:37
And according to the figure, what we have is that this angle here is 15 degrees.
01:49
Okay.
01:51
Notice that the forces that act on the pilot are the gravitational force and g pointing downwards and also the normal force, course, n.
02:03
Okay? and i'm setting up a coordinate system such that the y -axis points upwards and the x -axis to the right.
02:11
Okay, so in the y -coordinate, newton's second law tells us that and before anything else, notice that this angle here is 15 degrees.
02:25
So this means that in the by coordinate, we have n times sine of 15 minus m g is equal to zero, okay, because we are assuming that the only force that the only force that the pilot feels is the normal force...