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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
- (a) A very powerful vacuum cleaner has a hose 2.86 cm in diameter. With the end of the hose placed perpendicularly on the flat face of a brick, what is the weight of the heaviest brick that the cleaner can lift? (b) What If? An octopus uses one sucker of diameter 2.86 cm on each of the two shells of a clam in an attempt to pull the shells apart. Find the greatest force the octopus can exert on a clamshell in salt water 32.3 m deep.arrow_forwardAn inflated spherical beach ball with a radius of 0.3573 m and average density of 10.65 kg/m3 is being held under water in a pool by Janelle. The density of the water in the pool is 1000.0 kg/m3. When Janelle releases the ball, it begins to rise to the surface. If the drag coefficient of the ball in the water is 0.470 and the constant upward force on the ball is 1875 N, what will be the terminal speed of the ball as it rises? Ignore the effects of gravity on the ball.arrow_forwardA student suggests that the force of air resistance FA depends on the relative speed of an object passing through the air v according to FA = kvN, where k is a constant with appropriate units that depends on properties of the air and the size and shape of the object and N is a dimensionless exponent. The student has a hollow ball made of two hemispherical shells that can be connected together and disconnected, along with access to other commonly available materials. Write an experimental procedure that the student could follow to make measurements in order to find the value of N, and explain how a graph of In(FA) vs. In(v) could be used to find the values of k and N.arrow_forward
- Problem Like 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 vo- 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: = vo - which shows that velocity decreases in a linear manner.arrow_forwardKayaking is a great example of multiple drag forces. Where a person has to deal with currents in the water and air to propel themselves forward. In this problem, the water is moving at a velocity of 1.7 m/s directly in the direction you are trying to row. When considering this water, the area in contact with the water is .05 m^2, the drag coefficient is 1.02 with normal water density. You are moving at a velocity of 3 m/s, while the air is blowing against you with a velocity of 2.7 m/s (head wind). For the air, you have an area in contact of .5 m^2, and a drag coefficient of 1.75. Normal air density is present. In order to accomplish your time goal, you need a net force propelling you downstream of 175 newtons, how much force are you applying with the paddle to achieve this goal?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_forward
- A pulley is attached to one end of a rough plank, which makes an angle of 34◦ with the horizontal. A box is held at rest on the plank by a string that is attached to the box and passes over the pulley. A bucket of water is attached to the other end of the string and hangs freely. The coefficient of static friction between the plank and the box is 0.8. The box remains at rest but is on the point of slipping up the plank. The bucket of water has mass 7.5 kg.Name the four forces acting upon the box and draw a force diagram showing them, including the angles that show their directions.arrow_forwardA diving pool that is 4 m deep and full of water has a viewing window on one of its vertical walls. Find the force on a window that is a circle, with a radius of 2 m, tangent to the bottom of the pool. Use 1000 kg/m³ for the density of water and 9.8 m/s² for the acceleration due to gravity. Using the center of the window as the origin, find the width function w(y) for each value of y on the face of the window. w(y) =arrow_forwardA stubborn dog is being walked on a leash by its owner. At one point, the dog encounters an interesting scent at some spot on the ground and wants to explore it in detail, but the owner gets impatient and pulls on the leash with force F ⃗ = (98.0i ^ + 132.0j ^ + 32.0k ^ )N along the leash. (a) What is the magnitude of the pulling force? (b) What angle does the leash make with the vertical?arrow_forward
- A pulley is attached to one end of a rough plank, which makes an angle of 34° with the horizontal. A box is held at rest on the plank by a string that is attached to the box and passes over the pulley. A bucket of water is attached to the other end of the string and hangs freely. The coefficient of static friction between the plank and the box is 0.8. The box remains at rest but is on the point of slipping up the plank. The bucket of water has mass 7.5 kg. pulley box bucket of water 34° Model the box and the bucket of water as particles, the string as a model string and the pulley as a model pulley. (a) By considering the forces acting on the bucket of water, find the magnitude of the tension in the string (in newtons) in terms of g and the magnitude of the acceleration due to gravity (in ms-2). (b) State the four forces that act on the box and draw a force diagram showing them, including the angles that show their directions. (c) Take the unit vector i to be in the direction up the…arrow_forwardHow much force (in N) is exerted on one side of an 32.4 cm by 45.8 cm sheet of paper by the atmosphere? X N How can the paper withstand such a force? The paper can withstand this force because the atmosphere exerts an equal force on the surface of the other side of the paper in the opposite direction. The paper can withstand this force because its surface area is much smaller than that of the surrounding atmosphere. The paper can withstand this force because its density is much higher than that of the surrounding atmosphere. The paper can withstand this force because the atmosphere can only exert force on the surface of one side of the paper. +arrow_forwardCalculate the force (in N) a piano tuner applies to stretch a steel piano wire 8.60 mm, if the wire is originally 0.850 mm in diameter and 1.35 m long. Narrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning