A $4000$ kg truck is parked on a $15°$ slope. How big is the friction force on the truck? The coefficient of static friction between the tires and the road is $0.90$.

An Airbus $A320$ jetliner has a takeoff mass of $75,000$ kg. It reaches its takeoff speed of $82m/s(180mph)$ in $35$s. What is the thrust of the engines? You can neglect air resistance but not rolling friction

You're driving along at$25m/s$ with your aunt's valuable antiques in the back of your pickup truck when suddenly you see a giant hole in the road $55$ ahead of you. Fortunately, your foot is right beside the brake and your reaction time is zero!

a. Can you stop the truck before it falls into the hole?

b. If your answer to part a is yes, can you stop without the antiques sliding and being damaged? Their coefficients of friction are ${\mu }_{\mathrm{s}}=0.60$ and ${\mu }_{\mathrm{k}}=0.30$.

FIGURE EX$6.11$ shows the force acting on a $2.0kg$ object as it moves along the x-axis. The object is at rest at the origin at$t=0s.$ What are its acceleration and velocity at $t=6s$?

Large objects have inertia and tend to keep moving-Newton's BI0 first law. Life is very different for small microorganisms that swim through water. For them, drag forces are so large that they instantly stop, without coasting, if they cease their swimming motion. To swim at constant speed, they must exert a constant propulsion force by rotating corkscrew-like flagella or beating hair-like cilia. The quadratic model of drag of Equation $6.15$ fails for very small particles. Instead, a small object moving in liquid experiences a linear drag force, ${\overrightarrow{F}}_{\text{drag}}=(bv$, the direction opposite the motion), where $b$ is a constant. For a sphere of radius $R$, the drag constant can be shown to be $b=6\pi \eta R$, where $\eta$ is the viscosity of the liquid. Water at ${20}^{\circ }\mathrm{C}$ has viscosity $1.0\times {10}^{-3}\mathrm{Ns}/{\mathrm{m}}^2$.

a. A paramecium is about $100\mu \mathrm{m}$ long. If it's modeled as a sphere, how much propulsion force must it exert to swim at a typical speed of $1.0\mathrm{mm}/\mathrm{s}$ ? How about the propulsion force of a $2.0$-$\mu \mathrm{m}$-diameter $E$. coli bacterium swimming at $30\mu \mathrm{m}/\mathrm{s}$?

b. The propulsion forces are very small, but so are the organisms. To judge whether the propulsion force is large or small relative to the organism, compute the acceleration that the propulsion force could give each organism if there were no drag. The density of both organisms is the same as that of water, $1000\mathrm{kg}/{\mathrm{m}}^3$.

FIGURE EX$6.20$ shows the velocity graph of a $75$kg passenger in an elevator. What is the passenger’s weight

a. At $1$ s?

b. At $5$ s?

c. At $9$ s?