BackAn E. coli bacterium can be modeled as a 0.50 μm diameter sphere that has the density of water. Rotating flagella propel a bacterium through 40°C water with a force of 65 fN, where 1 fN = 1femtonewton = 10-15 N. What is the bacterium's speed in μm/s?
An object with cross section A is shot horizontally across frictionless ice. Its initial velocity is v₀ₓ at t₀ = 0 s. Air resistance is not negligible. Show that the velocity at time t is given by the expression .
A 1.0-cm-diameter, 2.0 g marble is shot horizontally into a tank of 20°C olive oil at 10 cm/s. How far in cm will it travel before stopping?
A 4.0-cm-diameter, 55 g ball is shot horizontally into a tank of 40°C honey. How long will it take for the horizontal speed to decrease to 10% of its initial value?
A spherical particle of mass m is shot horizontally with initial speed v₀ into a viscous fluid. Use Stokes' law to find an expression for vₓ (t), the horizontal velocity as a function of time. Vertical motion due to gravity can be ignored.
A medium-sized jet has a 3.8-m-diameter fuselage and a loaded mass of 85,000 kg. The drag on an airplane is primarily due to the cylindrical fuselage, and aerodynamic shaping gives it a drag coefficient of 0.37. How much thrust must the jet's engines provide to cruise at 230 m/s at an altitude where the air density is 1.0 kg/m3
So-called volcanic 'ash' is actually finely pulverized rock blown high into the atmosphere. A typical ash particle is a 50-μm-diameter piece of silica with a density of 2400 kg/m3. How long would it take this ash particle to fall from a height of 5.0 km in vacuum?
Below what speed does a 3.0-mm-diameter ball bearing in 20°C air experience linear drag?
Above what speed does a 3.0-mm-diameter ball bearing in 20°C water experience quadratic drag?
A ball is shot from a compressed-air gun at twice its terminal speed. What is the ball's initial acceleration, as a multiple of g, if it is shot straight up?
A 10 kg crate is placed on a horizontal conveyor belt. The materials are such that = 0.5 and = 0.3. Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up.
A 250 g ball is launched with a speed of 35 m/s at a 30° angle. A strong headwind exerts a constant horizontal drag force on the ball. What is the magnitude of the drag force if the wind reduces the ball's travel distance by 20%?
A 68-kg water skier is being accelerated by a ski boat on a flat ('glassy') lake. The coefficient of kinetic friction between the skier's skis and the water surface is μₖ = 0.25 (Fig. 5–59). What is the skier's acceleration if the rope pulling the skier behind the boat applies a horizontal tension force of magnitude FT = 240N to the skier (θ = 0°)?
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A 68-kg water skier is being accelerated by a ski boat on a flat ('glassy') lake. The coefficient of kinetic friction between the skier's skis and the water surface is μₖ = 0.25 (Fig. 5–59). What is the skier's horizontal acceleration if the rope pulling the skier exerts a force of FT = 240N on the skier at an upward angle θ = 12°?
A package of mass m is dropped vertically onto a horizontal conveyor belt whose speed is v = 1.5m/s, and the coefficient of kinetic friction between the package and the belt is μk = 0.70. For how much time does the package slide on the belt (until it is at rest relative to the belt)?