# 6.4 Drag force and terminal speed  (Page 6/12)

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A 60.0-kg and a 90.0-kg skydiver jump from an airplane at an altitude of $6.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\text{m}$ , both falling in the pike position. Make some assumption on their frontal areas and calculate their terminal velocities. How long will it take for each skydiver to reach the ground (assuming the time to reach terminal velocity is small)? Assume all values are accurate to three significant digits.

A 560-g squirrel with a surface area of $930\phantom{\rule{0.2em}{0ex}}{\text{cm}}^{2}$ falls from a 5.0-m tree to the ground. Estimate its terminal velocity. (Use a drag coefficient for a horizontal skydiver.) What will be the velocity of a 56-kg person hitting the ground, assuming no drag contribution in such a short distance?

${v}_{\text{T}}=25\phantom{\rule{0.2em}{0ex}}\text{m/s;}{\text{v}}_{2}=9.9\phantom{\rule{0.2em}{0ex}}\text{m/s}$

To maintain a constant speed, the force provided by a car’s engine must equal the drag force plus the force of friction of the road (the rolling resistance). (a) What are the drag forces at 70 km/h and 100 km/h for a Toyota Camry? (Drag area is $0.70\phantom{\rule{0.2em}{0ex}}{\text{m}}^{2}$ ) (b) What is the drag force at 70 km/h and 100 km/h for a Hummer H2? (Drag area is $2.44\phantom{\rule{0.2em}{0ex}}{\text{m}}^{2}\right)$ Assume all values are accurate to three significant digits.

By what factor does the drag force on a car increase as it goes from 65 to 110 km/h?

${\left(\frac{110}{65}\right)}^{2}=2.86$ times

Calculate the velocity a spherical rain drop would achieve falling from 5.00 km (a) in the absence of air drag (b) with air drag. Take the size across of the drop to be 4 mm, the density to be $1.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}{\text{kg/m}}^{3}$ , and the surface area to be $\pi {r}^{2}$ .

Using Stokes’ law, verify that the units for viscosity are kilograms per meter per second.

Stokes’ law is ${F}_{\text{s}}=6\pi r\eta v.$ Solving for the viscosity, $\eta =\frac{{F}_{\text{s}}}{6\pi rv}.$ Considering only the units, this becomes $\left[\eta \right]=\frac{\text{kg}}{\text{m}·\text{s}}.$

Find the terminal velocity of a spherical bacterium (diameter $2.00\phantom{\rule{0.2em}{0ex}}\text{μm}$ ) falling in water. You will first need to note that the drag force is equal to the weight at terminal velocity. Take the density of the bacterium to be $1.10\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}{\text{kg/m}}^{3}$ .

Stokes’ law describes sedimentation of particles in liquids and can be used to measure viscosity. Particles in liquids achieve terminal velocity quickly. One can measure the time it takes for a particle to fall a certain distance and then use Stokes’ law to calculate the viscosity of the liquid. Suppose a steel ball bearing (density $7.8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}{\text{kg/m}}^{3}$ , diameter 3.0 mm) is dropped in a container of motor oil. It takes 12 s to fall a distance of 0.60 m. Calculate the viscosity of the oil.

$0.76\phantom{\rule{0.2em}{0ex}}\text{kg/m}·\text{s}$

Suppose that the resistive force of the air on a skydiver can be approximated by $f=\text{−}b{v}^{2}.$ If the terminal velocity of a 50.0-kg skydiver is 60.0 m/s, what is the value of b ?

A small diamond of mass 10.0 g drops from a swimmer’s earring and falls through the water, reaching a terminal velocity of 2.0 m/s. (a) Assuming the frictional force on the diamond obeys $f=\text{−}bv,$ what is b ? (b) How far does the diamond fall before it reaches 90 percent of its terminal speed?

a. 0.049 kg/s; b. 0.57 m

(a) What is the final velocity of a car originally traveling at 50.0 km/h that decelerates at a rate of $0.400\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}$ for 50.0 s? Assume a coefficient of friction of 1.0. (b) What is unreasonable about the result? (c) Which premise is unreasonable, or which premises are inconsistent?

why is megaphone funnel shaped
velocity is a physician vector quantity; both magnitude and direction needed to define it. the scalar absolute value ( magnitude) of velocity is called "speed being a coherent derived unite whose quantity is measured in SI ( metric system) as metres per second (m/s) or SI base unit of (m . s^-1).
number of lines passing through area which is placed at some angle. these line are are produced by charge(+ or -).
hstjsbks
define electric flux? find the electric field due to a long strainght line
Clay Matthews, a linebacker for the Green Bay Packers, can reach a speed of 10.0 m/s. At the start of a play, Matthews runs downfield at 43° with respect to the 50-yard line (the +x-axis) and covers 7.8 m in 1 s. He then runs straight down the field at 90° with respect to the 50-yard line (that is, in the +y-direction) for 17 m, with an elapsed time of 2.9 s. (Express your answers in vector form.) (a) What is Matthews's final displacement (in m) from the start of the play?
What is his average velocity (in m/s)?
Justin
A machine at a post office sends packages out a chute and down a ramp to be loaded into delivery vehicles. (a) Calculate the acceleration of a box heading down a 17.4° slope, assuming the coefficient of friction for a parcel on waxed wood is 0.100. (b) Find the angle of the slope down which this box could move at a constant velocity. You can neglect air resistance in both parts.
what principle is applicable in projectile motion
does rocket and satellite follow the same principle??? which principle do both of these follow???
According to d'Broglie's concept of matter waves matter behaves like wave and the wavelength is h/p. but actually there is not only a wave but a wave packet wich is defined by a wave function and that wave function can defines everything about the particle but restricted by the uncertainty principle
what phenomenon describes Matter behave as a wave???
simple definition of wave
hello
can anyone help me with this problem
Carls
A projectile is shot at a hill, the base of which is 300 m away. The projectile is shot at 60°60° above the horizontal with an initial speed of 75 m/s. The hill can be approximated by a plane sloped at 20°20° to the horizontal. Relative to the coordinate system shown in the following figure, the equation of this straight line is y=(tan20°)x−109.y=(tan20°)x−109. Where on the hill does the projectile land?
Carls
what is velocity
hi, Musa,this moment a lateral