WILL RATE ANSWERS IMMEDIATELY!!!!! A.) A pilot, whose mass is 77.0 kg, makes a l

Question

WILL RATE ANSWERS IMMEDIATELY!!!!! A.) A pilot, whose mass is 77.0 kg, makes a loop-the-loop in a fast jet. Assume that the jet maintains a constant speed of 125 m/s and that the radius of the loop-the-loop is 0.637 km. What is the apparent weight that the pilot feels (i.e., the force with which the pilot presses against the seat) at the bottom of the loop-the-loop? What is the pilot's apparent weight at the top of the loop-the-loop? B.) A 5.10E+4 kg space probe is traveling at a speed of 10300 m/s through deep space. Retrorockets are fired along the line of motion to reduce the probe's speed. The retrorockets generate a force of 4.16E+5 N over a distance of 2410 km. What is the final speed of the probe? C.) A boat is pulled by two locomotives through a canal of length 1.94 km. The tension in each cable is 4.90E+3 N, and ? = 19.2

Explanation / Answer

There are two forces on the pilot, at the top & bottom of the circle;
His real weight "mg" , always acting straight down.
The normal force "N" of the seat pushing on the pilot, always acting perpendicular to the surfaces in contact. "N" is what you're after since from 3rd law it is numerically equal to the force the pilot pushes against the seat.
Take "IN" toward the center as positive and apply force law at the two positions;
TOP;
Nt + mg = mv^2/r
Nt = mv^2/r - mg

BOTTOM;
Nb - mg = mv^2/r
Nb = mg + mv^2/r

As you can see the force is smaller at the top. If the speed is large enough (so v^2/r = g) then the pilot experiences weightlessness. If v^2/r < g there would have to be another force, like a seatbelt, to keep him from falling out of the seat, since "N" from the seat can't be negative.

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