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.
Homework Statement
We have the equation for gravity due to the acceleration a = -GM/r2, calculate velocity and position dependent on time and show that v/x = √2GM/r03⋅(r/r0-1)
Homework Equations
x(t = 0) = x0 and v(t = 0) = 0
The Attempt at a Solution
v = -GM∫1/r2 dt
v = dr/dt
v2 = -GM∫1/r2...
Some time ago there was a similar thread
https://www.physicsforums.com/threads/clock-hypothesis-gravity-time-dilation-and-equivalence-principle.929838/
but what I want to discuss is similar but not the same and I would like to specify my question in such way, that it hopefully won't go sideways...
Homework Statement
A ball with a mass of 200g, is hanged on the roof of a bus with a rope (it's mass is negligible), when the bus starts moving, the rope makes an angle of 18°.
What's the acceleration of the bus?
Homework Equations
ΣF=m.a
The Attempt at a Solution
The first thing i thought of...
Homework Statement
Find the acceleration of a uniform solid sphere (of mass ##m## and radius ##R##) rolling without slipping down an incline at angle ##\alpha## using the Lagrangian method.
Homework Equations
Euler-Lagrange equation which says, $$\frac{\partial\mathcal{L}}{\partial...
1. Homework Statement
picture
Homework Equations
f=ma
The Attempt at a Solution
Below is my attempt for part B, i am not sure what i am doing wrong here but my answer is off for acceleration
In orbits it is said that ##\vec a \cdot \vec a' = |a||a'|##
How is this possible? Two vectors multiply to get scalars, and yet we cannot do the dot product literally because we do not know either of the components of ##\vec a## or ##\vec a'##.
Nor does the Angle Between Vectors Formula work...
Homework Statement
Three identical 4 kg crates are stacked one on top of the other. You want to accelerate them as much as possible by pushing on the lower crate, but the forces of static friction between the surfaces of the crates max out at 25 N. What is the maximum acceleration you can...
Homework Statement
Figure shows two blocks in contact sliding down an inclined surface of inclination 30.The friction coeffecient between the block of mass 2kg and the incline is μ=0.20 and that between block of mass 4kg and the incline is μ=0.30.Find the acceleration of 4 kg block (g=10m/s2)...
Homework Statement
I'm not understanding the difference between them, this is for Uniform Circular Motion.
Homework Equations
ar = -ac = -v2/r
The Attempt at a Solution
So what i know is radial acceleration goes in a direction towards the radius (perpendicular to velocity), and tangential...
Homework Statement
The coefficient of static friction between a tire and a dry road is about μs=0.85. What is the fastest you can safely drive the turn below?
a. Use a free-body diagram and force equations to determine the maximum force and acceleration you can achieve.
b. Use the map to...
Hello!
Why does resistance to acceleration depend on both the velocity of the object as well as the direction of the force?
In circular motion, we can measure the centripetal force and centripetal acceleration, then we can calculate objects mass. Speed remains constant.
But we would get the...
1. Homework Statement
Problem in pictures
Homework Equations
f=ma
The Attempt at a Solution
So the tension force is 20N, i took the frictional force on the bottom of the block as 3*9.8*.4 because the bottom of the block has a total mass of top block and bottom block = 3kg, so i have 20N -...
Homework Statement
African baobab trees can have circumferences of up to 43.0 m. Imagine riding a bicycle around a
tree this size. If, starting from rest, you travel a distance of 162 m around the tree with a constant
angular acceleration of 5.00 × 10–2 rad/s2, what will your final angular...
Homework Statement
11.10 The acceleration of a particle is directly proposional to the time t.
At t = 0, the velocity of the particle is v = 16 in./s. Knowing that v = 15 in./s
and that x = 20 in. when t = 1 s, determine the velocity, the position, and
the total distance traveled when t = 7s...
Howdy guys!
First I should probably introduce myself and give a little educational history, not necessarily so y'all can take pity on me and do my work for me, but so that you can understand the purpose of my question - I'd like to try and figure it out myself; I feel a great sense of...
Homework Statement
a) Calculate the kinetic energy required to accelerate a single proton from a rest position to 0.9999c. The mass of a proton is 1.67*10^-27 kg.
b) Find the ratio of the kinetic energy to the energy of a proton at rest.
c) Explain why no particle accelerator will ever be able...
And if so, how much? Should the radius be thought of as zero, an infinitesimal, or as the Planck length?
v2/r = ω2r
If its zero, then you immediately run into a problem when trying to calculate it with linear velocity.
v2/r = ar
v2/0 = undefined
OR
ω2r = ar
ω20 = 0
Which would mean that...
Is anyone aware of any theory which includes a theoretical limit on acceleration in the same way C is the universal speed limit?
[[By this I do not mean some sort of practical limit set by energy density and known systems of propulsion.]]
Homework Statement
Tarzan swings from a cliff at the end of a 20.0m vine that hangs from a high tree limb. Immediately after Tarzan steps off the cliff, the tension in the vine is 719N and makes an angle of 29.0deg with the vertical. Tarzan's weight is 822N.
What is the magnitude of Tarzan's...
So, we know that force equals mass times acceleration. A force is needed to cause an acceleration. I am wondering though, is mass required for accelerations to happen? Why or why not?
Homework Statement
A buzzing fly moves in a helical path given by the equation
r(t)=ib sin(wt) +jb cos(wt) + kct2
Show that the magnitude of the acceleration of the fly is constant, provided b, cc, and c are
constant.
Homework Equations
v = r/t
The Attempt at a Solution
Homework Statement
[/B]
The position of a particle as a function of time is given by
r(t) = i(1 - e^-kt ) + je^kt
where k is a positive constant. Find the velocity and acceleration of the particle. Sketch its trajectory.
Homework Equations
v (t) = dr/dt
a(t) = dv/dt
The Attempt at a Solution...
Homework Statement
At a playground you let your kid sister (30 kg) kneel on the surface (near the edge) of a 2.1 meter diameter merry-go-round. You push the merry-go-round so that it constantly accelerates from rest to a final speed of 1.7 rotations per second at the end of a 25 second...
I seem to be missing something very basic to the relationship between gravity and mass. If gravity is equivalent to acceleration, what is the basis for the acceleration that generates the gravitational force of an object such as the earth? What is accelerating? Am I even thinking about this in...
Homework Statement
A block of mass MB = 0.7 kg hangs from a string wrapped around a hoop that can rotate around its center. The hoop has a mass of MH = 1.3 kg and a radius of R = 0.4 m. The block descends under the influence of gravity. What is the magnitude of the acceleration of the mass in...
I have a problem where I have a large mass on wheels that I want to power with an electric motor. My hope is that I can find the torque i need to start and drive the motor and this is what I have so far.
Mass = 400t.
Initial velocity = 0
Final velocity = 2.5m/s
Distance required to travel =...
given: 128kg F1 = 28 N, F2 = 57 N, F3 = 38 N, θ1 = 30°, and θ3 = 60°.They are asking for the angle (measured relative to the positive direction of the x axis in the range of (-180°, 180°]) of the asteroid's acceleration?
The problem is displayed on quadrant I and IV
for vector notation I got...
Homework Statement :[/B]
Ok, so my exams are coming and all sorts of crazy thoughts are banging my mind and now I have a question regarding a very simple law of physics, the funniest part, this is my last month of high school life...so at this juncture of life, i am having this crazy question...
Homework Statement
Hydroelectric power station's turbine has a diameter of 7.5m, and a rotation frequency of 94 rotations per minute. What is the turbine's blades acceleration?
P.S. This is translated from another language
Homework Equations
a=4π2Rn2
Where n=rotational frequencyThe Attempt at...
The Earth is 1.50 × 1011 m from the sun. The earth's mass is 5.98 × 1024 kg, while the mass of the sun is 1.99 × 1030 kg.
What is Earth's acceleration toward the sun?
I'm really clueless how do this at all? I'm assuming it involves f=ma and GMm/r^2 formulas, but I really don't know. Help please...
Homework Statement
An ant clings to the outside edge of the tire of an exercise bicycle. When you start pedaling, the an't speed increases from ) to 10 m/s in 2.6 s. The wheel's rotational acceleration is 13 rad/s^s.
Determine the average tangential acceleration of the tire.
Homework...
Having a cylindrical iron container with wall thickness of 20 cm, and a total weight of 500 tons when filled with its cargo, how would you be able to calculate its required voltage and current input in a vertical railgun system (relative to the Moon's surface), with an exit acceleration of...
A frictionless incline (the triangle below) is bolted to the floor so that it can not move. A block of mass m slides down the slope, which makes an angle with the horizontal.a)Draw a free-body diagram for the block, labeling all forces uniquely.
b)Describe all the forces listed above in the...
In circular motions, one can measure the NetForce on an object with this formula:
ΣF = m*v^2/r.
But is this formula valid even if the orbital speed of the object is constantly increasing (or constantly decreasing)?
Homework Statement
A 24 kg object is placed at the top of an incline with height 500m and length 375m. The coefficient of kinetic friction is 0.600
1) Find the acceleration of the object.
2) Find the speed by the time it has reached the bottom of the inclined plane.
Homework Equations
F_g =...
What will be the difference in distance of the ball if it is hit by a club traveling 120 mph at impact (constant velocity) versus a ball hit by a club traveling at 120 mph but accelerating at the point of initial impact?
Hello!
Would love a quick explanation of these two exercises :)
1. Homework Statement
1) Find objects acceleration, when mass is 200kg and it is being pulled on a horizontal plane with a force of 2000N. How much work is done on 400m road?
2) An object fell from 200m. How much of its energy...
Homework Statement
Rank the rate at which the direction of each object's velocity is changing, greatest first.
Homework Equations
n/a
The Attempt at a Solution
I know a centripetal = v^2/r, but i don't have r so i am not sure if i am supposed to just eyeball it and draw a reference circle or...
Homework Statement
Homework Equations
W=mg
F=ma
The Attempt at a Solution
I'm not sure how I should be answering this problem, and the diagram itself looks odd. I was thinking about how it would work in real life, since the biggest pulley is attached to the leftmost pulley, by the same...
Hello.
I am in a 100 level physics college course and we are learning about conservation of energy. I am working with a program called Logger Pro. I've attached my data in the pictures. Here is a question that I am very much stuck on.
Using the Law of Conservation of Energy, show that the...
This is just a reality that I have stumbled upon that I'm sure was well-known, but I still found it interesting. I apologize if this is second-nature to physics experts.
I was responding to a post on a different thread that claimed you could make a tunnel around the Earth and if you sent a...
Homework Statement
A rocket is flying away from the Earth with a costant acceleration ##a## in a frame in which the rocket is at rest. Finding the equation of motion (the relation between the distance from the Earth and the terrestrial time). Showing that there is a maximum time ##T## after the...
Hi there,
I'm struggling to distinguish why the following two equations are giving distinct answers, when the question explicitly states either could be used:
v=u+at
v^2=u^2+ad
when
v=12 m/s
u=0 m/s
a (average acceleration)= the unknown variable
d=24 m
t=4s
Theoretically, the two should...
Homework Statement
What is the maximum acceleration the train can achieve?
Engine effect=6500kW
μ(Friction Coefficient (between rails and wheels))=0.45
g=9.82N/kg
m(Train weight)=120,000kg
α=0
Homework Equations
Fμ=Fn*μ
Fn=cos(α)*m*g
a=F/m
The Attempt at a Solution
We've used the equations...
Homework Statement
A Gak it a type of alien that lives on a planet in another galaxy. One day a Gak decides to find out a little more about his planet. He drops a ball (it starts at rest) with a mass of 4.88 kg and notes that it takes 0.712 s to fall a distance of 4.04 m.
What is the...
Homework Statement
For each of the following cases, represent on the trajectory, the velocity and tangential and normal components of the acceleration at times t1 and t2 of a mobile that moves according to the graph of s (arc) versus t (time) on the left. The point O on the trajectory marks the...
Homework Statement
What is the apparent weight of a 70-kg astronaut 3800 km from the center of the Earth's Moon in a space vehicle when
a) Moving at a constant velocity
b) Accelerating toward the Moon at 2.9 m/s^2?
State direction in each case
Homework Equations
wt = m(g+a)
wt = m(g-a)
Fgr =...
Homework Statement
[/B]
An X-ray tube gives electrons constant acceleration over a distance of 14 cm . If their final speed is 1.0×107 m/s , what are the electrons' acceleration?
Express your answer to two significant figures and include the appropriate units.
Homework Equations
My prof. has...
A race car strarts from rest and travels east along a straight and level track.
For the firs $5.0s$ of the cars motion,
the eastward compent of the car's velocity,is given by
$v_x(t)=(0.930 m/s^3)t^2 $
What is acceleration of the car when $v_x=14.5$
ok my first step with this was...
Hi.
The energy required to accelerate an object of mass ##m## to a speed ##v## is ##E_k=\frac{m}{2} v^2##. But how much energy does an object need to accelerate itself to ##v##? Say, how much fuel (in energy units) does a car need to accelerate to ##v##, if there are no air resistance or...