What is Kinematics: Definition and 1000 Discussions
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
A football player attempts a 30m field goal. If he is able to impart a velocity u of 30 m/s to the ball,compute the minimum angle θ for which the ball will clear the crossbar of the goal. (Hint: Let m = tanθ .)
Homework Equations
V0x = V cosθ
V0y = V sinθ
We get t...
Homework Statement
There are two rods with one having ring "P" and the other having ring "Q". The rings are connected by a massless and inextensible string which is then connected from "Q" to ceiling. If ring "Q" moves down with velocity "v", what is the velocity of ring "P" ? The string...
Homework Statement
A skidding car starts moving with a velocity of 6.75m/s at an angle of 58.82657 degrees north of east. Its velocity just before it comes out of its skid 4 seconds later is 3.25 m/s at an angle of 49.6091 degrees south of east. It travels with a constant acceleration while it...
Homework Statement
Runners A, B, and C run a 100-m race, each at a constant speed.
Runner A takes first place, beating runner B by 10 m. Runner
B takes second place, beating runner C by 10 m. By what time
interval does runner A beat runner C?
Homework Equations
d = 100 m
Δd = 10...
Homework Statement
A small car of mass m is released at height h on a steel track. The car rolls down the track and through a loop of radius R. At the end of the track, the car rolls off the track, which is positioned at a height H above the floor. Neglect friction and the small amount of...
Homework Statement
Rigid body
The plane rigid body ABCD shown in the figure has rectangular shape and
slides along the orthogonal runners X, Y. The points A and B are always in
contact with the ranners.
Data: ω=3 rad/s (angular velocity counterclockwise); \Theta=30°; AB=CD=1m;
AD=CB=0.5m...
Hi,
I have a generic question about solving kinematic problems using simple calculus. For eg.
A variable force F = bv (v is instantaneous speed at some time t) acts on a vehicle moving with speed v. Suppose the initial speed at t = 0 of the vehicle is v0. Calculate the distance through...
1. A car making a 99-km journey travels 38 km/h for the first 49.5 km. How fast must it go during the second 49.5 km to average 47 km/h?
2. Homework Equations ?
3. 47=.5(38+x)
Homework Statement
A bus starts moving with an acceleration of 2m/s^2. a cyclist, 96m behind the bus starts moving towards the bus simultaneously at 20m/s. in how much time will he overtake the bus.
Kindly point out the mistake in my solution too.
Homework Equations
v = u + at
s = ut + 1/2...
Homework Statement
Homework Equations
I'm dumbfounded by this problem. I can solve the (I think) harder problems with two fixed points and three rod segments. All the examples given in this book are of such "harder" problems and I have absolutely no example that resembles this...
Homework Statement
A particle with rest mass m_{0} and kinetic energy 3m_{0}c^{2} makes a completely inelastic collision with a stationary particle of rest mass 2m_{0}. What are the velocity and rest mass of the composite particle?
Homework Equations
T = (\gamma - 1)m_{0}c^{2} = E -...
1. Problem statement
2. Related equations
I = bmr^2
Energy equations (linear and rotational)
3. Attempt
Part a)
I know that the distance or height traveled by the box is [h - d] because center of the mass of box is just d. Initial kinetic energy of the box and cylinder is 0 and if only...
I'm working on an inverse kinematics problem (I make video games), and I'm reaching a bit beyond my education.
Right now, I've got an algorithm that solves the basic IK equation for a chain of rigid bodies connected by joints by approximately inverting ##J\Delta\theta = e##. Where ##\theta##...
I'm trying to learn some physics on my own, using the internet as my main source of information.
Now, I'm a bit confused about some terminology, and I can't find anything about it...
Distance vs displacement in rotational kinematics!
Is there a similar difference as in linear kinematics...
Homework Statement
This is from Kleppner, problem 1.12 in the 2010 edition, if you want to see the diagram.
The acceleration of gravity can be measured by projecting a body upward and measuring the time that it takes to pass two given points in both directions. Show that if the time the...
Homework Statement
An astronaut standing on a platform on the Moon
drops a hammer. If the hammer falls 6.0 meters vertically in 2.7 seconds, what is its acceleration?
Homework Equations
x=x0+v0t+(1/2)at2
The Attempt at a Solution
x=x0+v0t+(1/2)at2
6=0+.5(a)(2.72)
6=3.7a...
Hello,
I would like to learn how to calculate and simulate in Matlab inverse kinematics of manipulators.Can you please advise me some good websites or books. I am a beginner.
Thanks for any advice.
Here is the question:
Here is a link to the question:
Calculus Antiderivative problem.? - Yahoo! Answers
I have posted a link there to this topic so the OP can find my response.
Homework Statement
I'm studying for a Mechanics exam and I have a doubt on a 'Kinematics - Vector Derivative' exercise. I don't know how to begin and that's my main problem.
Well, this is the exercise:
Some data:
This mechanical system comprises:
- Body 1: A T-shaped arm, with...
Homework Statement
1. At t = 0, a particle leaves the origin with a velocity of 9.0 m/s in the positive y direction and moves in the xy plane with a constant acceleration of (2.0i - 4.0j) m/s2. At the instant the x coordinate of the particle is 15 m, what is the speed of the particle?
2...
Homework Statement
A Rock is dropped from a cliff and the sound of it striking the ocean is heard 3 seconds later. If the speed of sound in air is 340m/s, how high is the cliff?
Homework Equations
The linear kinematics of motion equations:
1. x-x_{0}=v_{0}t+\frac{1}{2}at^2
2...
A stone is dropped from the top of a building. Within the second before it hits the ground, it travels 1/5 of the building's height. Calculate the total height of the building.
Been trying to formulate simultaneous equations but there just doesn't seem to be enough information and too many...
Homework Statement
A missile is launched into the air at an initial velocity of 80 m/s. It is moving with constant velocity until it reaches 1000m, when the engine fails.
a) How long does it take it to reach 1000m
b)How high the missile go?
c)How long does it take for it to fall back to the...
Homework Statement
A 55 kg woman jumps to the floor from a height of 1.5 m.
If her body comes to rest during a time interval of 8.00 * 10^-3 seconds, what is the force of the floor on her feet?
Homework Equations
Unit conversion and
g = 9.8m.s^2 ~ 10 m/s^2
The Attempt at a...
Pictures of the questions are attached below.
For question 2, I totally cannot get any answer from the four choices after I substituted everything in the equation.
For question 4, I used V^2= U^2 + 2AS, with U being zero, A being 9.8 and S being 2.0. I got C but the answer is D. Can...
(this is all in context to a java 2d object and is not homework related)
I have an object with velocity v and position x.
Its acceleration is directly proportional to velocity squared ie a=k v^{2}.
Given the objects initial velocity u and its initial position x_{0} how would i work out its...
Physics Kinematics Homework Help!?
"While standing on a bridge 18.3 m above the ground, you drop a stone from rest. When the stone has fallen 2.50 m, you throw a second stone straight down. What initial velocity must you give the second stone if they are both to reach the ground at the same...
Homework Statement
As a prank, your friends have kidnapped you in your sleep, and transported you out onto the ice covering a local pond. Since you're an engineer, the first thing you do when you wake up is drill a small hole in the ice and estimate the ice to be 6.7cm thick and the distance...
Homework Statement
" An airplane turns slowly for 9.2s horizontally. The final velocity of the plane is 360km/hr [N]; the average acceleration during the turn is 5.0m/s^2 [W]. What is the initial velocity of the plane?"
Homework Equations
a=ΔV/t
The Attempt at a Solution
at=Δv...
Homework Statement
A 1.5-lb brick is released from rest A and slides down the inclined roof. If the coefficient of friction between the roof and the brick is μ=0.3, determine the speed at which the brick strikes the gutter G.
The Attempt at a Solution
These are the equations that I got...
Homework Statement
A hovercraft is traveling 3m/s at 180 deg. The fan of the hovercraft causes a=4m/s2 at 50° for 10 seconds.
Homework Equations
What is the final velocity?
The Attempt at a Solution
v = 3cos180 - 4cos50*10?
A light plane must reach a speed of 33 m/s for takeoff. How long must the runway be if the plane has a constant acceleration of 3.8 m/s2 ?so, I am new to kinomatic equations. We are using the 4 Basic ones.
need to see this one worked out if I may.Thanks
Homework Statement
Questions 19 and 20 refer to the following information
A particle of mass 2.00 kg moves under a force given by
F~ = −(8.00 N/m)(i + j)
where i and j are unit vectors in the x and y directions. The particle is placed at the origin with an initial velocity
v = (3.00 m/s)i +...
Homework Statement
Having aced your Physics 2111 class, you get a sweet summer-job working in the International Space Station. Your room-mate, Cosmonaut Valdimir tosses a banana at you at a speed of 14.0 m/s. At exactly the same instant, you fling a scoop of ice cream at Valdimir along...
1. Homework Statement
The velocity of a particle moving along the x-axis varies in time according to the expression
v(t)=α+βt2
α=46.4m/s
β=4.25m/s3
t is in seconds
Find the average acceleration in the time interval from t=0 to 3.63s.
Answer in units of m/s2
2. Homework...
Homework Statement
A particle moves along a straight line such that its acceleration is a = (4t2-2) \frac{m}{s^2}, where t is in seconds. When t = 0, the particle is located 1 m to the left of the origin, and when t = 2 s, it is 20 m to the left of the origin. Determine the position of the...
Homework Statement
The engineer of a passenger train traveling at 25.0 m/s sights a freight train whose caboose is 200 m ahead on the same track. The freight train is traveling at 15.0 m/s in the same direction as the passenger train. The engineer of the passenger train immediately applies the...
So the problem is:
a 1000 kg rocket is fired straight up, a 100 kg rocket is fired straight up with a constant acceleration for 16 seconds. It then stops accelerating and 20 seconds after launch reaches a height of 5100 m. Ignore air resistance.
Find the acceleration of the rocket for the...
Homework Statement
I am not going to use the exact same problem, as that would be cheating as this is for school, but Instead i will use an example problem:
A can of pop is tossed directly upwards with an initial velocity of 4 m/s. How high will it go?
Homework Equations
I know...
1. The distance from two airports is 1286 km by air. Plane A leaves the first airport at 10:00a heading north toward the second airport, another plane leaves from the second airport at 11:00a heading south towards the destination plane A originally departed from. Plane A travels at 720km/h, and...
http://www.examsolutions.net/a-level-maths-papers/Edexcel/Mechanics/Mechanics-M1/2010-June/paper.php
Q. 8
T = 3.36
a = 1.4
for part c)
First I found the velocity of A after it has moved for 0.5 s, and the displacement it has moved after 0.5 seconds:
I get that its velocity is...
Homework Statement
a particle travels along a straight line and the acceleration is given by
a = 30 - 0.2v
determine the time when the velocity of the particle is v = 30Homework Equations
\int \frac {dv}{ax+b} = \frac{1}{a} \ln (ax+b) The Attempt at a Solution
This is the solution from the...
The problem: (Note: the correct answer is bolded throughout)
A basketball is launched with an initial speed of 8 m/s at a 45 degree angle from the horizontal. The ball enters the basket in 0.96 seconds. What is the distance x and y?
Just ignore the distance x, I know it's simply the product...
Hi guys. I'm new here. If i did any mistake please forgive me.
First of all I have a simple problem need all of you to help me.
Here is the problem
The acceleration of a particle is defined by the relation a = -k√v, where k is constant.
Knowing that
x = 0 and v =...
Homework Statement
6) a helicopter blade spins at exactly 100 revolutions per minute. It's tip is 5.00m from the center of it's rotation. (a) calculate the average speed of the blade tip from the helicopters frame of reference. (b) What is it's average velocity over one revolution?
radius...
Homework Statement
{ y }_{ f }={ y }_{ i }+{ v }_{ yi }t+\frac { 1 }{ 2 } { a }_{ y }{ t }^{ 2 }\\ { v }_{ yf }={ v }_{ yi }+{ a }_{ y }t
Derive
{ { v }_{ yf } }^{ 2 }={ { v }_{ yi } }^{ 2 }+2{ a }_{ y }({ y }_{ f }-{ y }_{ i })
2. The attempt at a solution
This isn't an actual...
{ y }_{ f }={ y }_{ i }+{ v }_{ yi }t+\frac { 1 }{ 2 } { a }_{ y }{ t }^{ 2 }\\ { v }_{ yf }={ v }_{ yi }+{ a }_{ y }t
It almost looks like the second equation is the derivative of the first equation with respect to time.
Homework Statement
An electron is accelerated from rest to a velocity of 2.0x10^7 m/s.
a) if the electron traveled 0.10m while it was being accelerated, what was its acceleration?
b)How long did the electron take to attain its final velocity?
V1= 0m/s
V2= 2.0x10^7m/s
d= 0.10m
a=...