7. Friction, Inclines, Systems

Kinetic Friction

Open Question
An E. coli bacterium can be modeled as a 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 micrometers/s?
Open Question
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.a. Show that the velocity at time t is given by the expressionvₓ = v₀ₓ---------------1 + C𝓭pAv₀ₓt / 2m
Open Question
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?
Open Question
b. 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?
Open Question
a. 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.
Open Question
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/m^3
Open Question
So-called volcanic 'ash' is actually finely pulverized rock blown high into the atmosphere. A typical ash particle is a 50-micrometer-diameter piece of silica with a density of 2400 kg/m^3. (a) How long would it take this ash particle to fall from a height of 5.0 km in vacuum?
Open Question
(b) Below what speed does a 3.0-mm-diameter ball bearing in 20°C air experience linear drag?
Open Question
(a) Above what speed does a 3.0-mm-diameter ball bearing in 20°C water experience quadratic drag?
Open Question
A ball is shot from a compressed-air gun at twice its terminal speed.a. What is the ball's initial acceleration, as a multiple of g, if it is shot straight up?
Open Question
A 10 kg crate is placed on a horizontal conveyor belt. The materials are such that mu(s) = 0.5 and mu(k) = 0.3. (b) Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up.
Open Question
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%?
Open Question
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).
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(a) What is the skier's acceleration if the rope pulling the skier behind the boat applies a horizontal tension force of magnitude F_T = 240N to the skier (θ = 0°)?
Open Question
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).
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(b) What is the skier's horizontal acceleration if the rope pulling the skier exerts a force of F_T = 240N on the skier at an upward angle θ = 12° ?
Open Question
(II) 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.
(a) For how much time does the package slide on the belt (until it is at rest relative to the belt)?