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Suppose the object in Problem 70 had an initial velocity in the horizontal direction equal to the terminal speed, vx0 = mg/b. Show that the horizontal distance it can go is limited to xmax = mvx0/b, and find an expression for its trajectory (y as a function of x).
70. Moving through a liquid, an object of mass m experiences a resistive drag force proportional to its velocity, Fdrag = −bv, where b is a constant, (a) Find an expression for the object’s speed as a function of time, when it starts from rest and falls vertically through the liquid, (b) Show that it reaches a terminal velocity mg/b.
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Tutorials in Introductory Physics
- 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 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_forwardA skydiver of mass m = 60 kg jumps out of an airplane. At some moment before the 5. parachute opens, while falling in a spread-eagle formation, her instantaneous velocity is = (0,-20,0) m/s. (The coordinate system is one for which skyward is the +y direction.) What is the acceleration (a vector) of the skydiver at that moment? Include air drag in your calculation. Put your numerical vector answer in component form. Constants: In this formation her drag coefficient is C = 1.0. Her area that "catches" the air is A 1.5 m2. The density of air is p= 1.22 kg/m³.]arrow_forwardSimulate projectile motion with air resistance in PhysLab. A shuttlecock is launched from the ground with an initial speed of 36.8015 m/s at an angle of 7.0734 degrees with respect to the horizontal. The shuttlecock experiences air resistance with a drag coefficient of 0.1937 in an environment where the air density is 0.2178 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_forward
- Estimate the speed at which the drag on a 150-g steel ball becomes equal to about 1% of its weight. (The density of steel is about 7900 kg/m3, and C for a sphere is about equal to 0.5.) Take the density of air to be 1.2 kg/m3. The speed is m/s. 34. A space probe near the earth has values of E, L, and m such that L/m = 7.5 × 1010 m2/s and 2E/m = 0. Find the eccentricity of this orbit and the radius of the closest point of the orbit to the earth, and classify the orbit as elliptical, parabolic, or hyperbolic. The eccentricity of the orbit is______ and the orbit is ______Choose one (.Elliptical, Parabolic, Hyperbolic) The radius of the closest point of the orbit to the earth is _______ km.arrow_forwardSimulate projectile motion with air resistance. A shuttlecock is launched from the ground with an initial speed of 39.1416 m/s at an angle of 9.3878 degrees with respect to the horizontal. The shuttlecock experiences air resistance with a drag coefficient of 0.2891 in an environment where the air density is 0.8282 kg/m3. If the shuttlecock has a radius of 3.4 cm and a mass of 5.2 grams, what is the maximum heightreached by the shuttlecock? Assume that the experiment is done near the surface of the earth.arrow_forwardSimulate projectile motion with air resistance in PhysLab. A shuttlecock is launched from the ground with an initial speed of 33.5003 m/s at an angle of 8.0035 degrees with respect to the horizontal. The shuttlecock experiences air resistance with a drag coefficient of 0.111 in an environment where the air density is 0.6776 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_forward
- Simulate projectile motion with air resistance in PhysLab. A shuttlecock is launched from the ground with an initial speed of 39.8047 m/s at an angle of 9.7654 degrees with respect to the horizontal. The shuttlecock experiences air resistance with a drag coefficient of 0.1777 in an environment where the air density is 0.7779 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_forwardSimulate projectile motion with air resistance in PhysLab. A shuttlecock is launched from the ground with an initial speed of 37.186 m/s at an angle of 7.5661 degrees with respect to the horizontal. The shuttlecock experiences air resistance with a drag coefficient of 0.2807 in an environment where the air density is 0.546 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_forwardA 129 kg crate is sitting at the top of a ramp, which is inclined at an angle of 20 degrees with respect to the horizontal. Someone gives the crate a quick shove to get it moving, after which it slides down the ramp without any further assistance. The coefficient of kinetic friction between the crate and the ramp is ls = 0.23. What is the magnitude of the acceleration (in m/s?) of the crate?arrow_forward
- Please answer.arrow_forwardSimulate projectile motion with air resistance in PhysLab. A shuttlecock is launched from the ground with an initial speed of 31.9385 m/s at an angle of 8.2703 degrees with respect to the horizontal. The shuttlecock experiences air resistance with a drag coefficient of 0.2474 in an environment where the air density is 0.1483 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 (initHeight = 0) .arrow_forwardTo understand kinetic and static friction. A block of mass m lies on a horizontal table. The coefficient of static friction between the block and the table is μs. The coefficient of kinetic friction is μk, with μk<μs. Suppose you push horizontally with precisely enough force to make the block start to move, and you continue to apply the same amount of force even after it starts moving. Find the acceleration aaa of the block after it begins to move. Express your answer in terms of some or all of the variables μs, μk, and m, as well as the free-fall acceleration g.arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
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