# 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 the formula for pressure?
force/area
Kidus
force is newtom
Kidus
and area is meter squared
Kidus
so in SI units pressure is N/m^2
Kidus
In customary United States units pressure is lb/in^2. pound per square inch
Kidus
who is Newton?
scientist
Jeevan
a scientist
Peter
that discovered law of motion
Peter
ok
John
but who is Isaac newton?
John
a postmodernist would say that he did not discover them, he made them up and they're not actually a reality in itself, but a mere construct by which we decided to observe the word around us
elo
how?
Qhoshe
what is a scalar quantity
scalar: are quantity have numerical value
muslim
is that a better way in defining scalar quantity
Peter
thanks
muslim
quantity that has magnitude but no direction
Peter
upward force and downward force lift
upward force and downward force on lift
hi
Etini
hi
elo
hy
Xander
Hello
Jux_dob
hi
Peter
Helo
Tobi
what's the answer? I can't get it
what is the question again?
Sallieu
What's this conversation?
Zareen
what is catenation? and give examples
sununu
How many kilometres in 1 mile
Nessy
1.609km in 1mile
Faqir
what's the si unit of impulse
The Newton second (N•s)
Ethan
what is the s. I unit of current
Amphere(A)
imam
thanks man
Roland
u r welcome
imam
the velocity of a boat related to water is 3i+4j and that of water related to earth is i-3j. what is the velocity of the boat relative to earth.If unit vector i and j represent 1km/hour east and north respectively
what is head to tail rule?
kinza
what is the guess theorem
viva question and answer on practical youngs modulus by streching
send me vvi que
rupesh
a car can cover a distance of 522km on 36 Liter's of petrol, how far can it travel on 14 liter of petrol.
Isaac
yoo the ans is 193
Joseph
whats a two dimensional force
what are two dimensional force?
Where is Fourier Theorem?
what is Boyle's law
Boyle's law state that the volume of a given mass of gas is inversely proportion to its pressure provided that temperature remains constant
Abe
how do I turn off push notifications on this crap app?
Huntergirl
what is the meaning of in.
In means natural logarithm
Elom
is dea graph for cancer caliper experiment using glass block?
Bako
why the ship created in search way?
Mershak