What is Acceleration: Definition and 1000 Discussions
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time.
Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the orientation of the net force acting on that object. The magnitude of an object's acceleration, as described by Newton's Second Law, is the combined effect of two causes:
the net balance of all external forces acting onto that object — magnitude is directly proportional to this net resulting force;
that object's mass, depending on the materials out of which it is made — magnitude is inversely proportional to the object's mass.The SI unit for acceleration is metre per second squared (m⋅s−2,
m
s
2
{\displaystyle {\tfrac {\operatorname {m} }{\operatorname {s} ^{2}}}}
).
For example, when a vehicle starts from a standstill (zero velocity, in an inertial frame of reference) and travels in a straight line at increasing speeds, it is accelerating in the direction of travel. If the vehicle turns, an acceleration occurs toward the new direction and changes its motion vector. The acceleration of the vehicle in its current direction of motion is called a linear (or tangential during circular motions) acceleration, the reaction to which the passengers on board experience as a force pushing them back into their seats. When changing direction, the effecting acceleration is called radial (or orthogonal during circular motions) acceleration, the reaction to which the passengers experience as a centrifugal force. If the speed of the vehicle decreases, this is an acceleration in the opposite direction and mathematically a negative, sometimes called deceleration, and passengers experience the reaction to deceleration as an inertial force pushing them forward. Such negative accelerations are often achieved by retrorocket burning in spacecraft. Both acceleration and deceleration are treated the same, they are both changes in velocity. Each of these accelerations (tangential, radial, deceleration) is felt by passengers until their relative (differential) velocity are neutralized in reference to the vehicle.
I have a model of two slender rods (call them OA and AB) connected with a pin at A, anchored at O with a pin, and attached to horizontal slider at B. I am supposed to show graphs of different variables in Matlab as the angle theta changes. One of these steps is to show the acceleration of the...
Homework Statement
The acceleration amplitude of a damped harmonic oscillator is given by
$$A_{acc}(\omega) = \frac{QF_o}{m} \frac{\omega}{\omega _o} \sqrt{\it{R}(\omega)}$$
Show that as ##\lim_{\omega\to\infty}, A_{acc}(\omega) = \frac{F_o}{m}##
Homework Equations
$$\it{R}(\omega) =...
Homework Statement
A man is pulling himself up the 15 degree incline by the method shown. If the combined mass of the man and the cart is 100kg, determine the acceleration of the cart if the man excerpts 250 N on the rope. There is also a .2 coefficient for the kinetic friction between the...
Homework Statement
Sir Lost-a-Lot dons his armor and sets out from the castle on his trusty steed in his quest to improve communication between damsels and dragons (Fig. P12.20). Unfortunately his squire lowered the draw bridge too far and finally stopped it 20.0° below the horizontal...
Homework Statement
Homework Equations
∑Mb = m*a*d
The Attempt at a Solution
Using the formula below i get:
m*g*cos(0)*(0.07/2)-m*g*sin(0)*(195/2)=m*a*h
And I get 3.52 m/s^2
Is it correct?
There is a problem in my Physics textbook which says:
Homework Statement
"A car runs counter-clockwise in a circular lane of 1 km of diameter, going through the south extreme at 60 km/h on the instant t = 0. From that point onwards, the driver accelerates the car uniformely, reaching 240 km/h...
Homework Statement
A 1.5 kg ball is tied to a string that is .75 m long and whirled in a verticle circle.
A) Find the tension in the string at the top of the circle
B) Find the tension in the string at the bottom of the circle
Homework Equations
Fc=mac
ac= v2/r
The Attempt at a Solution
A)...
Hi I'm currently on the data analysis section of my MSc and I'm after some guidance if possible please. Basically I've managed to figure out many variables from force plate data including displacement/net force/velocity/power etc however I'm trying to do the same with data collected from a...
Homework Statement
A string is wrapped around a uniform solid cylinder of radius r, as shown in (Figure 1) . The cylinder can rotate freely about its axis. The loose end of the string is attached to a block. The block and cylinder each have mass m.
Find the magnitude α of the angular...
Homework Statement
All numerical constants are in the appropriate units, so that R (t) in units of meters, and a = 3.1 sec-1.
What is acceleration size (in meters per second ^ 2) t = 1 / 1.1 sec?
Note: When calculating sin (at), make sure the computer is in radian mode.
Homework Equations...
As far as I understand it, the Lorentz factor ##\gamma(\mathbf{v})## is constant when one transforms between two inertial reference frames, since the relative velocity ##\mathbf{v}## between them is constant.
However, I'm slightly confused when one considers four acceleration. What is the...
Homework Statement
what is the angular acceleration of the arm when theta equals 45 degrees.
v=2 m/s
picture is attached
Homework Equations
law of sites
law of cosinesThe Attempt at a Solution
[/B]
so I used the law of sines to resolve side r as being 579.555 mm
now I now I need to take time...
Hi everybody
Does anyone familiar with this equation?
Acceleration resistance,
= {(load MOI/mech. efficiency) + (motor MOI) x rpm^2} / {3.65 x 10^5 x acceleration time}
= {(kgm^2/ƞ) + (kgm^2) x rpm^2} / {3.65 x 10^5 x second}
= final value unit is in kilowatt (kW)
It used to calculate the...
Homework Statement
A new Tesla is designed that can perform a non-constant acceleration for 10 seconds of motion. The magnitude of the acceleration is given as a(t) = 1 m/s4t2
Starting from rest, how far does the car travel over this 10 second interval?
Homework Equations
This is what is...
Homework Statement
Suppose there is an object that is a distance ##r_0## from the center of a planet that is nearby (the object is outside the surface of the planet).
Let ## r ## represent the distance from the object to the planet's center.
Let ## t ## represent time.
The object, which is...
Hello guys. i know i shouldn't be doing this, but I am asking you if you can help me with a problem for my younger sister, because my major is something else (biology, genetics) and she need this and doesn't know how to solve it..
1. Homework Statement
At an upper end of the slope inclined at...
Homework Statement
If a proton with a kinetic energy of 6 MeV is traveling in a particle accelerator in a circular orbit of radius 0.75m, what fraction of its energy does it radiate per second?
m = 1.67 * 10^-27
epsilon_0 = 8.854 * 10^-12
c = 3 * 10^8
Homework Equations
dE/dt = (q^2 a^2) /...
Hi all!
I am taking an online course on aerial robotics and am currently on the topic of linearizing a 2-D quadrotor dynamic model. See slide (link below):
The equations under "linearized dynamics" are derived using the equilibrium hover configuration (e.g. y = y0, z = z0, Φ0 = 0, u1,0 =...
If the universe is expanding at an accelerating rate, either through a "pushing" or "pulling" force in a direction, and we have come from a "big bang point", then I wonder if we could calculate all our vectors at anyone moment and time to find the universal acceleration point and direction. If...
Homework Statement
"A drum of 60-mm radius is attached to a disk of 120-mm radius. The disk and drum have a total mass of 6 kg and a combined radius of gyration of 90 mm. A cord is attached as shown and pulled with a force P of magnitude 20 N. The disk rolls without sliding. Determine the...
How do i get an idea, or a 'feel' of the components of the acceleration in polar coordinates which constitute the component in the eθ direction?
from what i know, a= (r¨−rθ˙^2) er + (rθ¨+ 2r˙θ˙) eθ ;
(where er and eθ are unit vectors in the radial direction and the direction of increase of the...
I have been wondering, simple question, really: What is the relationship between momentum and centripetal acceleration, if there is one? Is there a relationship in terms of velocity, maybe, or is there none whatsoever?
Homework Statement
A pulley of radius, R and moment of inertia, I=2MR^2 is mounted on an axle with negligible friction. Block A, with a mass M, and Block B, with a mass of 3M, are attached to a light string that passes over the pulley. Assuming that the string doesn't slip on the pulley, Answer...
I've drawn the diagram of the forces exerted on and by a block resting on a floor.
For now, it seems that the forces exerted on the block are balanced - thus it doesn't accelerate.
The forces exerted on the floor are, however, not balanced. The floor is not accelerating downwards, I must then...
Homework Statement
Famous quarterback Fleet O. Floote is attempting a quarterback draw by running up the middle toward his goal line at 4.6 m/s. A linebacker hits him squarely, and their combined final velocity is 3.8 m/s at an angle of +120.° from the quarterback's original direction. The time...
Note: I didn't really know where to put this. It isn't a specific problem, but I've been asked by my physics teacher, who decided to give me and a few others an individual physics course of sorts, to find the means of solving similar problems. It's the first problem he assigned us, since we're...
Homework Statement
2 A particle P of mass mkg moves on an arc of a circle with centre O and radius a metres. At time t = 0
the particle is at the point A. At time t seconds, angle POA = sin^2 2t.
Find
(i) the value of t when the transverse component of the acceleration of P is first equal to...
Homework Statement
The velocity of an object moving along the x-axis is given by Vx = (2.0t-t2)m/s. Initially (at t=0), the object was at the origin.
a) Determine the object's acceleration at t=3.0s.
b) Find the object's position at t=3.0s
c) Calculate the object's maximum positive...
Homework Statement
An Atwood machine is a rope that passes over a pulley with a block attached to each end of the rope so that the blocks are not in contact with the floor. The frictionless axle of the pulley is oriented horizontally, and the rope is vertical save where it makes contact with...
Homework Statement
Large cockroaches can run as fast as 1.50 m/s in short bursts. Suppose you turn on the light in a cheap motel and see one scurrying directly away from you at a constant 1.50 m/s. If you start 0.91 m behind the cockroach with an initial speed of 0.82 m/s toward it, what...
Homework Statement
[/B]
A uniform cylinder with radius r is rolling down an incline without slipping as shown in diagram below. It's angular acceleration is α and acceleration of it's center of mass C is a. What will be the linear acceleration of point of contact P and another point Q on the...
A friend of mine posed a question to me the other day and I can't seem to wrap my head around it.
He's working with an electric stepper motor to turn a large thin disk, but he can't be sure of the torque required because to find the torque he needs the moment of inertia and the angular...
Recently, I was thinking about fusion and this thought struck my mind.
In tokamaks, the plasma is heated to extremely high temperatures in order to supply enough energy to the ions for them to fuse. But since, the plasma follows a Boltzmann maxwell distribution curve,only a few ions have have...
Homework Statement
If the masses for a double Atwood machine similar to the own shown in the attached picture are m1=2.0kg, m2=3.0kg, and m3=8.0kg: (a) what is the magnitude of the acceleration of the system and (b) how would you draw free-body diagrams for this problem?
NOTE: m3 does not...
Homework Statement
A small car with mass .800 kg travels at a constant speed of 12m/s on the inside of a track that is a vertical circle with radius 5.0m. If the normal force exerted by the track on the car when it is at the top of the track is 6.00N, what is the normal force at the bottom of...
Following scenario:
A rocket measuring 10 lightseconds in length accelerates near instantaneously to v=0.4c. Pre-acceleration two clocks placed at the endpoints of the rocket were synced.
What will be the time difference between the two clocks post acceleration?
I tried to figure it out...
EEE degree w/ phys minor.
hubble's graph shows velocity increasing over distance, not time.
an image 10 mil ly away is 10 mil y old (t = -d/c)
the origin of hubble's graph is d=0 and t=now, not 0
older images are faster and older image means younger galaxy
distance is proportional to age, which...
In another forum, the question was raised, "could a ship with 1G acceleration escape the gravity well of a planet with 1G gravity?"
A popular response is, if the craft is aerodynamic, it could accelerate laterally until it reached escape velocity and then manage to get to space.
I don't...
Hello everyone, first post! I'm not terribly fluent in these matters, I'll say to start, but I have a problem.
If a 3,219lb car is capable of accelerating at 40.2ft/s^2, or 0-60mph in 2.19 seconds
How much power must it be capable of producing?
Thanks for your time and patience! :)
Homework Statement
Two boxes with masses m_1 = 4 kg and m_2 = 10 kg are attached by a massless cord passing over a frictionless pulley as shown in in my picture. The incline is frictionless and thetha = 30 degrees
Homework Equations
f = ma
The Attempt at a Solution
[/B]
Tension 1 is...
Homework Statement
Hello
I have a video that is 30 fps according to the video information (when i right click on the file). It is stated that the videos were filmed in slow motion at 1/10 of normal speed.
I'm using a standard version of MATLAB to plot points (actual position) on a moving...
Homework Statement
An 82 kg couch is being pushed with a force of 56 N at an angle of 40o above horizontal. Friction is to be considered. Draw a free-body diagram representing this scenario.If the coefficient of friction between the couch and the floor is 0.051, what is the acceleration of...
Two masses, m and M, are a fixed distance R apart. One of the masses is much larger then the other. At time t the masses start to fall towards each other. Using Newton's Law of Gravitation we can determine the acceleration of the small mass. Can one use the Schwarzschild metric in the...
Homework Statement
Approaching one of the many sharp horizontal turns in the Monaco Grand Prix, an experienced Formula-1 driver slows down from 135 km/h to 55 km/h while rounding the bend in 10 s. If the driver continues to decelerate at this same rate and the radius of the curve is 15 m, what...
Homework Statement
A child swings a tennis ball attached to a .750 m-string in a horizontal circle above his head at a rate of 5.00 rev/s What is the centripetal acceleration of the tennis ball?
Homework Equations
angular speed \omega = 2pi/T
speed = r\omega
a_c = -v^2 /r
a_c = -\omega ^2...
Hey, orbital mechanics!
I can't find what I need to figure this out on the internet, and I don't do calculus so I don't understand all that I find. Help me make my next sci-fi novel plausible?
I just did an Oberth maneuver around Sol, 21 radii (.0977 AU, 14,616,000 km) from center...
1. For the following, the x-axis is not allowed to be set along the ramp. If a mass, starting from rest, slides along a linear, frictionless incline of length D and then falls a distance h to the ground, will it have an x-component of acceleration?
2. Relevant kinematics formulas?
3. I...
I'm new to this, so I'm sorry if I am doing this process incorrectly. I feel like the answer to this should be straightforward and should just be √(2Lgsinθ). For some reason, I thought there was an acceleration vector along the ramp made up of x and y components, but I don't think this is...
I've been trying to figure out this seemingly simple problem for a theoretical project I'm doing, but can't figure it out.
Homework Statement
This isn't real, but say that a vehicle travels from 0 to 200 feet linearly at a non-constant acceleration of 32.17 m/s^2 (1g), but the acceleration is...