7. Friction, Inclines, Systems

You push on a 3-kg box to give it an initial speed of 5 m/s across a floor. If μ_k = 0.3, how far does the box travel before coming to a stop?

A $45.0$-kg crate of tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it, and the crate just begins to move when your force exceeds $313$ N. Then you must reduce your push to $208$ N to keep it moving at a steady $25.0$ cm/s. What are the coefficients of static and kinetic friction between the crate and the floor?

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?

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

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. Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up.