Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. The study of how forces act on bodies falls within kinetics, not kinematics. For further details, see analytical dynamics.
Kinematics is used in astrophysics to describe the motion of celestial bodies and collections of such bodies. In mechanical engineering, robotics, and biomechanics kinematics is used to describe the motion of systems composed of joined parts (multi-link systems) such as an engine, a robotic arm or the human skeleton.
Geometric transformations, also called rigid transformations, are used to describe the movement of components in a mechanical system, simplifying the derivation of the equations of motion. They are also central to dynamic analysis.
Kinematic analysis is the process of measuring the kinematic quantities used to describe motion. In engineering, for instance, kinematic analysis may be used to find the range of movement for a given mechanism and working in reverse, using kinematic synthesis to design a mechanism for a desired range of motion. In addition, kinematics applies algebraic geometry to the study of the mechanical advantage of a mechanical system or mechanism.
Homework Statement
Hello, after searching the internet I found this very active community and hope you can help me with my problem.
On the Khan Academy website (Which I highly recommend) there are exercises such as Kinematic Equations. I was asked to solve Vi (Initial velocity) so I used the...
Homework Statement
I am attempting to write a physics simulation program using the kinematic equations and using Runge-Kutta to solve them to determine how an object will move through space subject to certain gravitational forces etc.
Homework Equations
I have x=vt+(at^2)/2 as the equation i...
What is solution to this problem any help is appreciated. Thanks
Around wheel that can rotate around a horizontal axis is coiled (reeled) light unstretchable rope whose other end is tied load P. The position of the body is determined at all time with coordinate z =(pi)t³/3. Determine current...
Homework Statement
A racket ball is struck in such a way that it leaves the racket with a speed of 5.37 m/s in the horizontal direction. When the ball hits the court, it is a horizontal distance of 2.15 m from the racket. Find the height of the racket ball when it left the racket...
I have been looking into how the overall viscosity of a liquid/gas is related to kinematic and dynamic viscosities.
I have used nwater = 1e-3 Pa.s
nair = 17.4e-6 Pa.s
densitywater = 1000 kgm^-3
densityair = 1.3 kgm^3
and kinematic viscosity v = n/density
So vair ~ 1.4e-5
vwater ~...
An elevator ascends from the ground with uniform speed. At time T1 a marble is droped from the floor and hits the ground T2 seconds later. Find the height of the elevator at time T1? Clue T1=T2=4s.
Z0=V0z*T1
Z=V0z*T2 - (g*(T2)^2)/2.
Where Z0 is the height at T1, Z is taken to be...
pls see attached file.
so i thought i could use this eqn:
aA = w2 AO en + alpha AO et
but when i try to work out w, something goes wrong. i do:
w = 7.16605 (normal velocity i found by having the given velocity as a y coordinate one, then resolving for normal/tangential) / 0.25. but...
Homework Statement
A car accelerates uniformly from an initial velocity for 6s. The displacements in the 3rd and the 5th seconds are 12m and 18m respectively. Find the acceleration and the initial velocity of the car.
(Answer: 3m/s^2 , 4.5 m/s)
Btw this from a first year physics course...
Homework Statement
A .1 m ramp is sitting at the edge of a horizontal surface that is 1 m from the ground. One ball is resting at the top of a ramp and another ball is resting at the bottom of the ramp where it is flattened. Each ball has a mass of .05 kg. Ball one is released and hits ball...
Mechanics Kinematic General Concept question, not a numerical!?
I'm really confused concerning the positive direction and the acceleration taken while concerning the motion of the ball!
Well, the main thing that i wanted to ask is that if 2 balls are been projected at the same time in two...
Homework Statement
Let a and b be two given orthonormal vectors around a fixed point O. The motion of a continuum is defined by the following velocity field:
[tex] v(M) = \alpha \vec{a} (\vec{b} . \vec{OM}) \\ [\tex]
where [tex] \alpha [\tex] is a known positive constant.
1...
A motorcycle officer hidden at an intersection observes a car driven by an oblivious driver who ignores a stop sign and continues through the intersection at constant speed. The police officer takes off in pursuit 1.95 s after the car has passed the stop sign. She accelerates at 4.2 m/s2 until...
A person runs 100 m in 9.77 s. Maximum speed was reached in 3 s, then maintained for the rest of the time. What was the acceleration during the first 3 seconds?
I know that I can find the average velocity, which is 100 m/9.77 s, and i know that initial velocity is 0 m/s. I don't know how to...
Vectors and 2D Kinematic Question!
On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a golf club improvised from a tool. The free-fall acceleration on the moon is 1/6 of its value on earth. Suppose he hits the ball with a speed of 25 m/s at an angle of 35° above...
Homework Statement
A stone is flung straight up from a point 1.50 m above the ground and with an initial speed of 19.6 m/s.
a. What is the stone's maximum height above the ground?
b. How much time passes before the stone hits the ground?
Homework Equations
The four kinematic equations...
Homework Statement
A light elastic string has natural length 1 m. One end of the string is attached to the fixed point O and particle P of mass 4 kg is suspended from the other end of the string. When hanging in equilibrium, P is 6/5 m below O. Find the modulus of elasticity of the string...
Hey guy,
I'm working at my school to ID our collection of kinematic models and make signs for explaining them. I have them almost done, but there are a few I can't find in any of the books, can you guys take a look at the attached and linked pictures and see if you can ID them?
Homework Statement
a man dropped a stone into a can that is 120m deep. if the temperature of the air is 20degree celsius. how long would it take for a man to hear the sound when the stone hit the can?
Homework Equations
d=Vi*t + 1/2*a*t^2
The Attempt at a Solution
since i know that...
In this particular act, a man is shot out of a cannon with an initial velocity of 10 m/s at an angle of 60 degrees onto a net at some distance away. The cannon is 6.5m above the ground, and the net is 2.5m above the ground.
How long does it take for the man to land on the net?
how far is the...
Homework Statement
Runner A runs at 6.0 m/s for 10 s. How far does he go?
NOTE: THE ANSWER IS 60 m BUT I DON'T KNOW HOW IT GOT TO THAT.
Homework Equations
V=Vo + at
X=1/2(Vo +V)T
X=VoT + 1/2at2
V2=Vo2 + 2ax
(If a 2 is after a letter then it means squared)
X=displacement...
Homework Statement
Equation for a particle moving in one dimension with potential energy U(x):
t=\int1/\sqrt{2(E-U(x))/m} , integrated from x0 to 5x0
Suppose U(x)=c/x for x>0. Calculate the time for the particle to move from x0 to 5x0, starting from rest at x0. Leave the answer in...
What is the difference between Kinematic coupling in Abaqus and Rigids in Nastran?
Why it is named as Kinematic Coupling... what is the physics behind the word kinematic and rigids?
Homework Statement
A car driving at a constant speed of 75 ft/s passes a police car that is initially at rest. If the police car decides to give chase
A) What rate would the police have to accelerate to catch up with the other car in 12 seconds?
B) What is the police car's speed at the end...
Homework Statement
A helicopter carrying Dr. Evil takes off with a constant upward acceleration of 5.0m/s². Secret agent Austin Powers jumps on just as the helicopter lifts off the ground. After the two men struggle for 10.0s, Powers shuts off the engine and steps out of the helicopter...
Homework Statement
1. A car driving at a constant speed of 75 ft/s passes a police car that is initially at rest. If the police car decides to give chase
A) What rate would the police have to accelerate to catch up with the other car in 12 seconds?
B) What is the police car's speed at the end...
Homework Statement
Ok, so i have a test on Kinematics Grade 11 coming up on monday and i want some practise on Challenging Word Problems. Can anyone give me some problems to prepare for mondays test and help me through the process like which formula i use and stuff.
Homework Equations...
Here is the problem that I am having trouble with (It probably is a no brainer, but i am a bit rusty- not a bit actually, a lot!).
Here is the question:
A student stands at the top of a building to perform a kinematics experiment. He throws a red ball directly upwards with an initial speed...
Ok, pretty basic Physics-101 question. However, I don't understand why my method for solving isn't working.
Homework Statement
Two cars. Car one is at rest, while the car two is traveling at a constant 16.66 m/s (given as 60 km/hr). At the moment car two passes car one, car one begins...
This question is part of a lab report I've been working on, sorry in advance if I didn't follow all guidelines here.
1. Homework Statement
Explain what the shape of the graph tells you about the mathematical relationship between displacement and average velocity. Include the kinematic equation...
I already typed a long drawn out post, so I am going to simplfy it.
I am having trouble using algebra to rearrange equation.
For Example,
v=d/t
And so, to solve for both t and d, I do the following
vt=d/t x t
vt=d
vt/v=d/v
t=d/v
I have difficulty with most if not all the other...
Homework Statement
A rectangular block of length L is traveling on a smooth surface at velocity u. When it encounters rough ground with coefficient of friction mu, it decelerates to a stop. What is the time taken for the rectangular block to stop?Homework Equations
F= (mu)mgThe Attempt at a...
Homework Statement
What is the thrown angle of a body with a weight w, to make the maximun height equal to the horizontal lenght. Also exists a horizontal wind's force F that acts over the body?
The Attempt at a Solution
I think these are the relations, or i am wrong?
1...
Homework Statement
An arresting device on a carrier deck stops an airplane in 1.5s. The average acceleration was 49 m/s^2. What was the stopping distance? What was the initial speed?
Homework Equations
?
[b]3. The Attempt at a Solution [/b
DONE! :D
No need for help anymore :D
I was just pondering today how the kinematic equation for position looks like a taylor expansion.
x = x0 + dx/dt *t + (1/2)*d2x/dt2*t2
I believe it continues like that, exactly like a taylor expansion does, so the next term would be (1/6)*d3x/dt3*t3
If it is indeed a taylor expansion, what...
Homework Statement
A body of mass m is thrown upward with intial velocity u, in a medium which exerts a resistance force of mkv. Express, in term of g, k and u, the time taken for the body to reach its maximum height
Homework Equations
The Attempt at a Solution
a = -g - kv...
Homework Statement
A particle of mass m falls from rest; the resistance of the air when the speed is v is kv2 where k is a constant. Show that after a time t, the velocity v and the time t are related by the equation t = V/2g ln[(V + v )/(V - v)] where V2
= mg/k
Homework Equations...
Homework Statement
A particle of mass m is projected vertically upwards, with an initial speedo of u, in a medium which exerts a resistance of magnitude mkv, where k is a positive constant and v is the speed of the particle after time t. Express, in terms of k, g and u, the time taken for the...
In Euclidean Space-Time, the kinematic equation is:
s^2=g_{\mu\nu}x^{\mu}x^{\nu}
am i correct if i write :
K^{\mu \nu}_{\mu \nu}=g_{\mu \nu}x^{\mu}x^{\nu}
where s^2=K^{\mu \nu}_{\mu \nu}?
thank you very much
Okay, we all know that
ΔX = ViT + 1/2AT^2
Say I drop a stone from rest and I want to find its distance at a given time knowing the acceleration. Since the initial velocity is zero and its accelerating vertically we can say.
ΔY = 1/2AT^2
ΔY = (AT^2) / 2 <------------------------- Keep in mind...
Hello,
Just wondering if someone can help me make sense of something. I realize it's probably a simple problem, but my math skills aren't the best and I can't see through it.
I'm trying to end up with this kinematic equation:
X= Xo + Vo(t-to) + 1/2(a)(t-to)^2
And to do this the...
Homework Statement
The driver of a vehicle on a level road determined that she could increase her speed from rest to 50 mph in 35 sec and from rest to 65 mph in 95 sec. Assume that acceleration varies linearly with speed (with a non zero intercept). Determine the max acceleration in each case...
Homework Statement
A mountain climber stands at the top of a 50.0m cliff hanging over a calm pool of water. The climber throws two stones vertically 1.0 s apart and observes that they cause a single splash when they hit the water. The first stone has an initial velocity of + 2.0 m/s.
a) How...
Homework Statement
David is driving a steady 30.0 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.0 m/s^2 at the instant when David passes.
a. How far does Tina drive before passing David?
b. What is her speed as she passes him?
Velocity...
If I drop a ball, how far will it fall in 2 seconds?
ΔX = ViT + 1/2AT^2
ΔX = (0)(2) + 1/2(9.8)(2)^2
ΔX = 19.6 m
I tested this, and there is no way an object falls 19.6 m in only 2 seconds. Think about it. Drop something right now and it will only fall like 1 meter in one second. I don't...
Hi, I have been reading a book regarding modelling vehicle behaviour using multi-body systems.
It discusses the use of points, vectors, local and global co-ordinate systems as well as assigning degrees of freedom to various parts. I am pretty confident with the whole concept but I am unsure...
Homework Statement
An observer on the Earth observes the angle subtended by the diameter of the moon to be 0.009199 radians. If the moon is 234,800 miles away, what is its diameter?
Homework Equations
The Attempt at a Solution
Not quite sure where to begin with this one. I think it...
Homework Statement
Knowing and understanding the kinematic equation's variables x1, x0, v0, t, and a, how has .5 been incorporated into the equation?
I realized this unknown during lab. Now, as I've nearly completed my analysis, I find that the values I've derived for acceleration should be...