# 6.4 Drag force and terminal speed  (Page 10/12)

 Page 10 / 12

Two blocks connected by a string are pulled across a horizontal surface by a force applied to one of the blocks, as shown below. The coefficient of kinetic friction between the blocks and the surface is 0.25. If each block has an acceleration of $2.0\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}$ to the right, what is the magnitude F of the applied force?

25 N

As shown below, the coefficient of kinetic friction between the surface and the larger block is 0.20, and the coefficient of kinetic friction between the surface and the smaller block is 0.30. If $F=10\phantom{\rule{0.2em}{0ex}}\text{N}$ and $M=1.0\phantom{\rule{0.2em}{0ex}}\text{kg}$ , what is the tension in the connecting string?

In the figure, the coefficient of kinetic friction between the surface and the blocks is ${\mu }_{\text{k}}.$ If $M=1.0\phantom{\rule{0.2em}{0ex}}\text{kg,}$ find an expression for the magnitude of the acceleration of either block (in terms of F , ${\mu }_{\text{k}},$ and g ).

$a=\frac{F}{4}-{\mu }_{k}g$

Two blocks are stacked as shown below, and rest on a frictionless surface. There is friction between the two blocks (coefficient of friction $\mu$ ). An external force is applied to the top block at an angle $\theta$ with the horizontal. What is the maximum force F that can be applied for the two blocks to move together?

A box rests on the (horizontal) back of a truck. The coefficient of static friction between the box and the surface on which it rests is 0.24. What maximum distance can the truck travel (starting from rest and moving horizontally with constant acceleration) in 3.0 s without having the box slide?

14 m

A double-incline plane is shown below. The coefficient of friction on the left surface is 0.30, and on the right surface 0.16. Calculate the acceleration of the system.

## Challenge problems

In a later chapter, you will find that the weight of a particle varies with altitude such that $w=\frac{mg{r}_{0}{}^{2}}{{r}^{2}}$ where ${r}_{0}{}^{}$ is the radius of Earth and r is the distance from Earth’s center. If the particle is fired vertically with velocity ${v}_{0}{}^{}$ from Earth’s surface, determine its velocity as a function of position r . ( Hint: use ${a}^{}dr={v}^{}dv,$ the rearrangement mentioned in the text.)

$v=\sqrt{{v}_{0}{}^{2}-2g{r}_{0}\left(1-\frac{{r}_{0}}{r}\right)}$

A large centrifuge, like the one shown below, is used to expose aspiring astronauts to accelerations similar to those experienced in rocket launches and atmospheric reentries. (a) At what angular velocity is the centripetal acceleration 10 g if the rider is 15.0 m from the center of rotation? (b) The rider’s cage hangs on a pivot at the end of the arm, allowing it to swing outward during rotation as shown in the bottom accompanying figure. At what angle $\theta$ below the horizontal will the cage hang when the centripetal acceleration is 10 g ? ( Hint: The arm supplies centripetal force and supports the weight of the cage. Draw a free-body diagram of the forces to see what the angle $\theta$ should be.)

A car of mass 1000.0 kg is traveling along a level road at 100.0 km/h when its brakes are applied. Calculate the stopping distance if the coefficient of kinetic friction of the tires is 0.500. Neglect air resistance. ( Hint: since the distance traveled is of interest rather than the time, x is the desired independent variable and not t . Use the Chain Rule to change the variable: $\frac{dv}{dt}=\frac{dv}{dx}\phantom{\rule{0.2em}{0ex}}\frac{dx}{dt}=v\frac{dv}{dx}.\right)$

78.7 m

An airplane flying at 200.0 m/s makes a turn that takes 4.0 min. What bank angle is required? What is the percentage increase in the perceived weight of the passengers?

A skydiver is at an altitude of 1520 m. After 10.0 seconds of free fall, he opens his parachute and finds that the air resistance, ${F}_{\text{D}}$ , is given by the formula ${F}_{\text{D}}=\text{−}bv,$ where b is a constant and v is the velocity. If $b=0.750,$ and the mass of the skydiver is 82.0 kg, first set up differential equations for the velocity and the position, and then find: (a) the speed of the skydiver when the parachute opens, (b) the distance fallen before the parachute opens, (c) the terminal velocity after the parachute opens (find the limiting velocity), and (d) the time the skydiver is in the air after the parachute opens.

a. 53.9 m/s; b. 328 m; c. 4.58 m/s; d. 257 s

In a television commercial, a small, spherical bead of mass 4.00 g is released from rest at $t=0$ in a bottle of liquid shampoo. The terminal speed is observed to be 2.00 cm/s. Find (a) the value of the constant b in the equation $v=\frac{mg}{b}\left(1-{e}^{\text{−}bt\text{/}m}\right),$ and (b) the value of the resistive force when the bead reaches terminal speed.

A boater and motor boat are at rest on a lake. Together, they have mass 200.0 kg. If the thrust of the motor is a constant force of 40.0 N in the direction of motion, and if the resistive force of the water is numerically equivalent to 2 times the speed v of the boat, set up and solve the differential equation to find: (a) the velocity of the boat at time t ; (b) the limiting velocity (the velocity after a long time has passed).

a. $v=20.0\left(1-{e}^{-0.01t}\right);$ b. ${v}_{\text{limiting}}=20\phantom{\rule{0.2em}{0ex}}\text{m/s}$

what is friction
a force act by surface between two bodies whose are always oppose the relative motion .....
Raghav
when two rough bodies are placed in contact and try to slip each other ... than a force act them and it's ippse the relative motion between them
Raghav
thats friction force and roughnes of both bodies is define friction of surface
Raghav
what is a progressive wave
What is the wake for therapist
can u like explain your question with clear detail
Chikamso
who would teach me vectors?
what's chemistry
branch of science dt deals with the study of physical properties of matter and it's particulate nature
Josiah
Good
Daniel
actually
Nathz
Y acctually do u hav ur way of defining it? just bring ur iwn idear
Daniel
well, it deals with the weight of substances and reaction behind them as well as the behavior
Josiah
buh hope Esther, we've answered ur question
Josiah
what's ohms law
CHIJIOKE
ohms law states that, the current flowing through an electric circuit is directly proportional to the potential difference, provided temperature and pressure are kept constant
Josiah
what is sound
James
ohms law states that the resistance of a material is directly proportional to the potential difference between two points on that material, if temperature and other physical conditions become constant
Chikamso
How do I access the MCQ
As I think the best is, first select the easiest questions for you .and then you can answer the remaining questions.
lasitha
I mean I'm unable to view it
Abraham
when I click on it, it doesn't respond
Abraham
ohhh,try again and again ,It will be showed
lasitha
okay
Abraham
what is centripetal force
هي قوة ناتجة من الحركة الدائرية ويكون اتجاهها إلى المركز دائماً
meaning of vector quantity
vector quantity is any quantity that has both magnitude in terms of number (units) and direction in terms of viewing the quantity from an origin using angles (degree) or (NEWS) method
LEWIS
vector quantity is physical quantity has magnitude and direction
vector is a quantity that is use in measuring size of physical properties and their direction
Bitrus
what difference and similarities between work,force,energy and power?
Anes
power
mehreen
power
saba
enery is the ability to do work. work is job done, force is a pull or push. power has to do with potential. they belong to different categories which include heat energy, electricity.
Andrew
force refers to a push or pull... energy refers to work done while power is work done per unit time
Shane
mathematically express angular velocity and angular acceleration
it depends on the direction. an angular velocity will be linear and angular acceleration will be an angle of elevation.
Andrew
The sonic range finder discussed in the preceding question often needs to be calibrated. During the calibration, the software asks for the room temperature. Why do you suppose the room temperature is required?
Suppose a bat uses sound echoes to locate its insect prey, 3.00 m away. (See [link] .) (a) Calculate the echo times for temperatures of 5.00°C5.00°C and 35.0°C.35.0°C. (b) What percent uncertainty does this cause for the bat in locating the insect? (c) Discuss the significance of this uncertainty an
Shaina
give a reason why musicians commonly bring their wind instruments to room temperature before playing them.
Shaina
The ear canal resonates like a tube closed at one end. (See [link]Figure 17_03_HumEar[/link].) If ear canals range in length from 1.80 to 2.60 cm in an average population, what is the range of fundamental resonant frequencies? Take air temperature to be 37.0°C,37.0°C, which is the same as body tempe
Shaina
By what fraction will the frequencies produced by a wind instrument change when air temperature goes from 10.0°C10.0°C to 30.0°C30.0°C ? That is, find the ratio of the frequencies at those temperatures.
Shaina
what are vector quantity
Quantities that has both magnitude and direction
NNAEMEKA
what is lenses
Rhoda
vector quantities are those physical quantites which have magnitude as well as direction and obey the laws of vector algebra.
Huzaif
electric current has both magnitude and direction but it doesn't obey the laws of vector algebra, hence it is not a vector quantity.
Huzaif
what is momentum
Momentum=mv
Nana
what is dimension
what is vector
A quantity having both magnitude and direction
Zubair
quality having both magnitude and direction
ZINA
they have magnitude and direction.
Andrew
What is biology
Jimmy
Jimmy nkhoma
Jimmy
What is biology
Jimmy
what is math
Tamzid
Biology is d study of living things
Nana