tried multiple times, can\'t figure it out please help! A jet traveling at a spe

Question

tried multiple times, can't figure it out please help! A jet traveling at a speed of 1.80 102 m/s executes a vertical loop with a radius of 5.25 102 m. (See Figure (b).) Find the magnitude of the force of the seat on a 70.0-kg pilot at the following positions. (a) the top of the loop 70.0 Incorrect: Your answer is incorrect. Draw a free-body diagram of the pilot and note that there are only two forces on him. However, information about the motion of the plane lets us know his acceleration, which then allows us to find the strength of the force of the seat. Note the direction of the acceleration. N (b) the bottom of the loop 9399 Incorrect: Your answer is incorrect. Draw a free-body diagram of the pilot and note that there are only two forces on him. However, information about the motion of the plane lets us know his acceleration, which then allows us to find the strength of the force of the seat. Note the direction of the acceleration. N

Explanation / Answer

The acceleration of something in circular motion is given by: a = v^2 / r Where v is the velocity and r the radius. So you can easily plug in numbers to find the acceleration due to the loop if you ignore the acceleration of gravity for a moment. a = (1.80*10^2 m/s)^2 / (5.25*10^2 m) Which gives an acceleration of 61.71 m/s^2. At the top of the loop, we subtract the acceleration of gravity, which is 9.81m/s^2 : a - gravity which gives an acceleration of 51.9 m/s^2. At the bottom of the loop, we *add* the acceleration of gravity: a + gravity which gives an acceleration of 71.52 m/s^2 So, we now have the accelerations. But the question asks for the *force* on a 70 kg pilot. So we just use the force equation: F = m a Multiplying the accelerations we obtained above by the pilot's mass, (a) We get a force at the top of the loop = 70*51.9 = 3633 N (b) Force at the bottom = 70*71.52 = 5006.4 N

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