7. Friction, Inclines, Systems

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?

What is the primary cause of kinetic friction between two surfaces in contact?

Pushing a 10-kg toolbox across the floor, you find that the box moves at a constant speed when you push horizontally with a force of 39 N. What is the coefficient of kinetic friction between the floor and the toolbox?

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 push must you exert to give it an acceleration of $1.10$ m/s²?

As you push a cereal box across a tabletop, the sliding friction acting on the cereal box

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 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 μ_k = 0.70. For how much time does the package slide on the belt (until it is at rest relative to the belt)?

What is the magnitude of the acceleration of a skydiver at the instant she is falling at one-half her terminal speed?

In a laboratory experiment on friction, a $135$-N block resting on a rough horizontal table is pulled by a horizontal wire. The pull gradually increases until the block begins to move and continues to increase thereafter. Figure E$5.26$ shows a graph of the friction force on this block as a function of the pull. Identify the regions of the graph where static friction and kinetic friction occur.

You throw a baseball straight upward. The drag force is proportional to $v^2$. In terms of $g$, what is the $y$-component of the ball's acceleration when the ball's speed is half its terminal speed and it is moving up?

Above what speed does a 3.0-mm-diameter ball bearing in 20°C water experience quadratic drag?

So-called volcanic 'ash' is actually finely pulverized rock blown high into the atmosphere. A typical ash particle is a 50-$\mu m$-diameter piece of silica with a density of 2400 kg/m³. How long in hours does it take this ash particle to fall from a height of 5.0 km in still air? Use the properties of 20°C air at sea level.

An 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?

Police investigators, examining the scene of an accident involving a car and an old truck, measure 72-m-long skid marks for the truck, which nearly came to a stop before colliding with the car at rest. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of the truck assuming a level road.

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). Explain why the skier's acceleration in part (b) is greater than that in part (a).