# 6.4 Drag force and terminal speed  (Page 8/12)

 Page 8 / 12

If the order of the barges of the preceding exercise is reversed so that the tugboat pulls the $3.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\text{-kg}$ barge with a force of $20.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{N},$ what are the acceleration of the barges and the tension in the coupling cable?

An object with mass m moves along the x -axis. Its position at any time is given by $x\left(t\right)=p{t}^{3}+q{t}^{2}$ where p and q are constants. Find the net force on this object for any time t .

m (6 pt + 2 q )

A helicopter with mass $2.35\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}\phantom{\rule{0.2em}{0ex}}\text{kg}$ has a position given by $\stackrel{\to }{r}\left(t\right)=\left(0.020\phantom{\rule{0.2em}{0ex}}{t}^{3}\right)\stackrel{^}{i}+\left(2.2t\right)\stackrel{^}{j}-\left(0.060\phantom{\rule{0.2em}{0ex}}{t}^{2}\right)\stackrel{^}{k}.$ Find the net force on the helicopter at $t=3.0\phantom{\rule{0.2em}{0ex}}\text{s}\text{.}$

Located at the origin, an electric car of mass m is at rest and in equilibrium. A time dependent force of $\stackrel{\to }{F}\left(t\right)$ is applied at time $t=0$ , and its components are ${F}_{x}\left(t\right)=p+nt$ and ${F}_{y}\left(t\right)=qt$ where p , q , and n are constants. Find the position $\stackrel{\to }{r}\left(t\right)$ and velocity $\stackrel{\to }{v}\left(t\right)$ as functions of time t .

$\stackrel{\to }{v}\left(t\right)=\left(\frac{pt}{m}+\frac{n{t}^{2}}{2m}\right)\stackrel{^}{i}+\left(\frac{q{t}^{2}}{2}\right)\stackrel{^}{j}$ and $\stackrel{\to }{r}\left(t\right)=\left(\frac{p{t}^{2}}{2m}+\frac{n{t}^{3}}{6m}\right)\stackrel{^}{i}+\left(\frac{q{t}^{3}}{60m}\right)\stackrel{^}{j}$

A particle of mass m is located at the origin. It is at rest and in equilibrium. A time-dependent force of $\stackrel{\to }{F}\left(t\right)$ is applied at time $t=0$ , and its components are ${F}_{x}\left(t\right)=pt$ and ${F}_{y}\left(t\right)=n+qt$ where p , q , and n are constants. Find the position $\stackrel{\to }{r}\left(t\right)$ and velocity $\stackrel{\to }{v}\left(t\right)$ as functions of time t .

A 2.0-kg object has a velocity of $4.0\stackrel{^}{i}\phantom{\rule{0.2em}{0ex}}\text{m/s}$ at $t=0.$ A constant resultant force of $\left(2.0\stackrel{^}{i}+4.0\stackrel{^}{j}\right)\phantom{\rule{0.2em}{0ex}}\text{N}$ then acts on the object for 3.0 s. What is the magnitude of the object’s velocity at the end of the 3.0-s interval?

9.2 m/s

A 1.5-kg mass has an acceleration of $\left(4.0\stackrel{^}{i}-3.0\stackrel{^}{j}\right)\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}.$ Only two forces act on the mass. If one of the forces is $\left(2.0\stackrel{^}{i}-1.4\stackrel{^}{j}\right)\phantom{\rule{0.2em}{0ex}}\text{N,}$ what is the magnitude of the other force?

A box is dropped onto a conveyor belt moving at 3.4 m/s. If the coefficient of friction between the box and the belt is 0.27, how long will it take before the box moves without slipping?

1.3 s

Shown below is a 10.0-kg block being pushed by a horizontal force $\stackrel{\to }{F}$ of magnitude 200.0 N. The coefficient of kinetic friction between the two surfaces is 0.50. Find the acceleration of the block. As shown below, the mass of block 1 is ${m}_{1}=4.0\phantom{\rule{0.2em}{0ex}}\text{kg,}$ while the mass of block 2 is ${m}_{2}=8.0\phantom{\rule{0.2em}{0ex}}\text{kg}\text{.}$ The coefficient of friction between ${m}_{1}$ and the inclined surface is ${\mu }_{\text{k}}=0.40.$ What is the acceleration of the system? $5.4\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}$

A student is attempting to move a 30-kg mini-fridge into her dorm room. During a moment of inattention, the mini-fridge slides down a 35 degree incline at constant speed when she applies a force of 25 N acting up and parallel to the incline. What is the coefficient of kinetic friction between the fridge and the surface of the incline?

A crate of mass 100.0 kg rests on a rough surface inclined at an angle of $37.0\text{°}$ with the horizontal. A massless rope to which a force can be applied parallel to the surface is attached to the crate and leads to the top of the incline. In its present state, the crate is just ready to slip and start to move down the plane. The coefficient of friction is $80%$ of that for the static case. (a) What is the coefficient of static friction? (b) What is the maximum force that can be applied upward along the plane on the rope and not move the block? (c) With a slightly greater applied force, the block will slide up the plane. Once it begins to move, what is its acceleration and what reduced force is necessary to keep it moving upward at constant speed? (d) If the block is given a slight nudge to get it started down the plane, what will be its acceleration in that direction? (e) Once the block begins to slide downward, what upward force on the rope is required to keep the block from accelerating downward?

a. 0.60; b. 1200 N; c. $1.2\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}$ and 1080 N; d. $-1.2\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2};$ e. 120 N

#### Questions & Answers

a particle projected from origin moving on x-y plane passes through P & Q having consituents (9,7) , (18,4) respectively.find eq. of trajectry.
rahul Reply
definition of inertia
philip Reply
the reluctance of a body to start moving when it is at rest and to stop moving when it is in motion
charles
An inherent property by virtue of which the body remains in its pure state or initial state
Kushal
why current is not a vector quantity , whereas it have magnitude as well as direction.
Aniket Reply
why
daniel
the flow of current is not current
fitzgerald
bcoz it doesn't satisfy the algabric laws of vectors
Shiekh
The Electric current can be defined as the dot product of the current density and the differential cross-sectional area vector : ... So the electric current is a scalar quantity . Scalars are related to tensors by the fact that a scalar is a tensor of order or rank zero .
Kushal
what is binomial theorem
Tollum Reply
hello are you ready to ask aquestion?
Saadaq Reply
what is binary operations
Tollum
What is the formula to calculat parallel forces that acts in opposite direction?
Martan Reply
position, velocity and acceleration of vector
Manuel Reply
hi
peter
hi
daniel
hi
Vedisha
*a plane flies with a velocity of 1000km/hr in a direction North60degree east.find it effective velocity in the easterly and northerly direction.*
imam
hello
Lydia
hello Lydia.
Sackson
What is momentum
isijola
hello
Saadaq
A rail way truck of mass 2400kg is hung onto a stationary trunk on a level track and collides with it at 4.7m|s. After collision the two trunk move together with a common speed of 1.2m|s. Calculate the mass of the stationary trunk
Ekuri Reply
I need the solving for this question
philip
is the eye the same like the camera
EDWIN Reply
I can't understand
Suraia
same here please
Josh
I think the question is that ,,, the working principal of eye and camera same or not?
Sardar
yes i think is same as the camera
muhammad
what are the dimensions of surface tension
samsfavor
why is the "_" sign used for a wave to the right instead of to the left?
MUNGWA Reply
why classical mechanics is necessary for graduate students?
khyam Reply
classical mechanics?
Victor
principle of superposition?
Naveen Reply
principle of superposition allows us to find the electric field on a charge by finding the x and y components
Kidus
Two Masses,m and 2m,approach each along a path at right angles to each other .After collision,they stick together and move off at 2m/s at angle 37° to the original direction of the mass m. What where the initial speeds of the two particles
MB
2m & m initial velocity 1.8m/s & 4.8m/s respectively,apply conservation of linear momentum in two perpendicular directions.
Shubhrant
A body on circular orbit makes an angular displacement given by teta(t)=2(t)+5(t)+5.if time t is in seconds calculate the angular velocity at t=2s
MB
2+5+0=7sec differentiate above equation w.r.t time, as angular velocity is rate of change of angular displacement.
Shubhrant
Ok i got a question I'm not asking how gravity works. I would like to know why gravity works. like why is gravity the way it is. What is the true nature of gravity?
Daniel Reply
gravity pulls towards a mass...like every object is pulled towards earth
Ashok
An automobile traveling with an initial velocity of 25m/s is accelerated to 35m/s in 6s,the wheel of the automobile is 80cm in diameter. find * The angular acceleration
Goodness Reply
(10/6) ÷0.4=4.167 per sec
Shubhrant
what is the formula for pressure?
Goodness Reply
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

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