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Stokes' law describes sedimentation of particles in liquids and can be used to measure viscosity. Particles in liquids achieve terminal velocity quickly. One can measure the time it takes for a particle to fall a certain distance and then use Stokes' law to calculate the viscosity of the liquid. Suppose a steel ball bearing (density
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- 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 paratrooper and his 8-m-diameter parachute weigh 950 N. Taking the average air density to be 1.2 kg/m3, determine the terminal velocity of the paratrooper.arrow_forwardIf a bubble in sparkling water accelerates upward at the rate of 0.225 m/s2 and has a radius of 0.500 mm, what is its mass? Assume that the drag force on the bubble is negligible.arrow_forward
- A circular hoop of radius R made of thin wires of different linear densities. Half hoop has density u1 and the other half u2. When a point mass m is placed at the center of the hoop point O, find the net force that the hoop acts on marrow_forwardA 60 kg skydiver can be modeled as a rectangular "box" with dimensions 22 cm × 40 cm × 1.8 m. What is his terminal speed if he falls feet first? Suppose that the density of air is 1.2 kg/m3.arrow_forwardA baseball has a terminal speed of 42 m/s in air (ρ = 1.2 kg/m3). What would be its terminal speed in water (ρ = 1.0 x 103 kg/m3)? Group of answer choices 42 m/s 1.5 m/s 1200 m/s 18 m/s 0.05 m/sarrow_forward
- The Mariana trench is located in the Pacific Ocean at a depth of about 11 000 m below the surface of the water. The density of seawater is 1025 kg/m3. (a) If an underwater vehicle were to explore such a depth, what force would the water exert on the vehicle's observation window (radius = 0.129 m)? (b) For comparison, determine the weight of a jetliner whose mass is 1.91 × 105 kg. (a) Number Units (b) Number Unitsarrow_forwardFind the terminal velocity of a spherical bacterium (diameter 2.00 µm ) falling in water. You will first need to note that the drag force is equal to the weight at terminal velocity. Take the density of the bacterium to be 1.10×103 kg/m3 .arrow_forwardFind the terminal velocity of a spherical bacterium (diameter 2.00 μm ) falling in water. You will first need to note that the drag force is equal to the weight at terminal velocity. Take the density of the bacterium to be 1.10 × 103 kg/m3 .arrow_forward
- On 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_forwardIn the figure, a tin of anti-oxidants (m1 = 4.7 kg) on a frictionless inclined surface is connected to a tin of corned beef (m2 = 2.4 kg). The pulley is massless and frictionless. An upward force of magnitude F = 6.4 N acts on the corned beef tin, which has a downward acceleration of 4.7 m/s2. What are (a) the tension in the connecting cord and (b) angle β?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning