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Your sailboat has capsized! Fortunately, you are no longer aboard the boat. Instead, you are hanging onto the end of a long rope, the other end of which is attached to a Coast Guard helicopter. Model yourself as a particle of mass M = 55.0 kg with a diameter equal to 0.500 m. The density of the air is ρ = 1.29 kg/m3. Assume the drag coefficient between you and the air is C = 0.500. a. First, ignore the drag force due to the air. If the helicopter is flying at a constant speed v0 = 35.0 m/s, what angle will the rope make with the vertical? b. Now, consider the drag force due to the air. What angle does the rope make with the vertical given the information in part (a)?
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Chapter 6 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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- A shuttlecock is launched from the ground with an initial speed of 38.9424 m/s at an angle of 7.8623 degrees with respect to the horizontal. The shuttlecock experiences air resistance with a drag coefficient of 0.2339 in an environment where the air density is 0.0559 kg/m3. If the shuttlecock has a radius of 3.4 cm and a mass of 5.2 grams, what is the maximum height reached by the shuttlecock? Assume that the experiment is done near the surface of the earth.arrow_forwardLike friction, drag force opposes the motion of a particle in a fluid; however, drag force depends on the particle's velocity. Find the expression for the particle's velocity v(x) as a function of position at any point x in a fluid whose drag force is expressed as Fdrag = kmv where k is a constant, m is the mass of the particle and v is its velocity. Assume that the particle is constrained to move in the x-axis only with an initial velocity v0. Solution: The net force along the x-axis is: ΣF = -F = m then: -mv = m Since acceleration is the first time derivative of velocity a = dv/dt, -mv = m We can eliminate time dt by expressing, the velocity on the left side of the equation as v = dx/dt. Manipulating the variables and simplifying, we arrive at the following expression / = -k "Isolating" the infinitesimal velocity dx and integrating with respect to dx, we arrive at the following: = v0 - which shows that velocity decreases in a linear manner.arrow_forwardOn a part-time job, you are asked to bring a cylindrical iron rod of density 7800 kg/m^3, length 89.2 cm and diameter 2.45 cm from a storage room to a machinist. Calculate the weight of the rod, w. Assume the free-fall acceleration is g = 9.80 m/s^2. Express you answer in N.arrow_forward
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