What is Kinematic equations: Definition and 111 Discussions
Kinematics equations are the constraint equations of a mechanical system such as a robot manipulator that define how input movement at one or more joints specifies the configuration of the device, in order to achieve a task position or end-effector location. Kinematics equations are used to analyze and design articulated systems ranging from four-bar linkages to serial and parallel robots.
Kinematics equations are constraint equations that characterize the geometric configuration of an articulated mechanical system. Therefore, these equations assume the links are rigid and the joints provide pure rotation or translation. Constraint equations of this type are known as holonomic constraints in the study of the dynamics of multi-body systems.
I tried to write the data I understood from the image:
y0=160m
yf=0
x0=0
x1=192m
I tried to express the total change in time using the position over time equation on the Y direction:
y(t)=y0+v0y*(t2-t1)-0.5a(t2-t1)^2
but then I stuck with 2 variables and didn't know what to do
any help?
Givens:
Vyi=12.5 m/s
Vyf=-12.5 m/s (at the same horizontal level)
ay=-9.81 m/s^2
Δy= zero m (as the displacement on the y-axis, when the projectile reaches the same horizontal level, is zero m)
Δt=?
When I use
Δy=[(vyi+vyf)/2]*Δt
I get the time as undefined.
Δt= 2Δy/(vyi+vyf)
= 2*0 m/(12.5...
I was able to solve for the velocity of MB and got my answer as 4.47m/s.
The main issue right now for me is how to get the angles. I'm really confused on what most people have been posting as we didn't get a groundwork on this topic and so most of the basics I had them self taught.
So far I...
I have tried this problem over 4 times and keep getting the exact same answer, which is incorrect. Could someone please help by pointing out what I did wrong, or letting me know if I am actually on the completely wrong path?
Thanks!
Have a wonderful day :)
Derek Muller is the Veritasium YouTube channel host and he had a wager against UCLA professor Alexander Kusenko on whether a unpowered car going downwind can go faster than the wind.
Derek Muller said it can go faster than the wind, while Alexander Kusenko said it only seems that way because...
Figure 1. A map of the crime scene.
My attempt:We start by trying to map the possible throwing area from the green marked walls in the figure. The area can be divided into two suitable triangles from each corner towards the red marked crime scene. With the help of Google Earth, the sides of...
Details of Question:
ds/dt= v which becomes ds=v dt, where s=displacement, t =time, and v=velocity
Then we can integrate both sides of this equation, and do a little algebra, and turn the above equation into:
s − s0 = v0t + ½at2
My main question is about the integration of...
1. I'm trying to calculate the time at which the crash does not happen (if possible, because I don't know the official solution. I assume the crash is preventable).
At the time t the truck decelerates and makes the distance ##s_2= \frac{v_2^2}{2a}##. In the same time the car drives with the...
I've been attempting to solve this problem for three days now. I have thrown away my old attempts (like, scrumpled up into the bin), but my old attempts involved:
Trying to set up simultaeneous equations relating the journeys between EH and FG to find the deceleration, but the reason why this...
Part A)
So, I set the two positions equations of A and B equal to each other since the position has to be the same.
A: 0 + 0 + 1/2(2)t^2 = 50 + 0 + 1/2(4)t^2 :B
I know I have to solve for time t, but there's no way to solve it with both sides having t^2 so I am not sure which variables I got...
Magnitude of acceleration of system:
a = (4.59kg - 1.71kg)(9.81N/kg)/(4.59kg + 1.71kg)
= 4.48 m/s^2
Velocity of lighter mass when heavier one hits the ground:
vf^2 = vi^2 + 2ad
= 0 + 2(4.48m/s^2)(2.60m)
vf = 4.83 m/s [up]
I am not sure what to do from here? I don't really understand what...
I recently watched a video on youtube where a guy fires a 50 cal. rifle straight up into the air and measures the time of flight at about 100s. It got me thinking about what altitude the round reached. So I used the kinematics equations and obtained a value of 12.25km. Amazing, but I wondered...
My question is why isn't the radial component e→r of acceleration in cylindrical coords simply r'' ?
If r'' is the rate at which the rate of change of position is changing in the radial direction, wouldn't that make it the radial acceleration? I.e, the acceleration of the radius is the...
Homework Statement
What happens to the distance traveled in the same amount of time as an object accelerates?Homework Equations
None[/B]The Attempt at a Solution
None[/B]
Homework Statement
A catapult launches a rock with an initial velocity of 50m/s at 35 degrees above the horizontal. The rock must clear 3.5m at 10m away in order to make it over a castle wall to get to the enemy. Do the knights succeed? By how much do they clear the wall or miss clearing the...
Homework Statement
A stone is thrown off of a bridge that is 40m above the water. The stone lands 48m from the base of the bridge. The stone was thrown with an initial velocity of 15m at 30 degrees above the horizontal.
What is the maximum height the stone reaches above the water? (ans:42.87m)...
Homework Statement
A ball is thrown off of a building in the +x direction at 10m/s. If the ball takes 2s to land, how tall is the building?
Homework Equations
Vf=Vi(a)(t)
Δd=Vi(t)+1/2(a)(t)
Vf^2=Vi^2+2(a)(Δd)
Δd=1/2(Vf-Vi)(t)
The Attempt at a Solution
Vf: 0m/s
Vi: 10m/s
a: -9.8m/s^2
t: 2s...
Homework Statement
A ball is kicked with an initial speed of 20m/s at an angle of 50° above the horizontal. What maximum height does the ball reach?
Homework Equations
Vfx=VicosΘ
Δx=VicosΘt
Vfy=(VisinΘ)+ay⋅t
(Vfy)^2=(VisinΘ)^2+2ay⋅Δy
Δy=1/2(Vfy+(VisinΘ))⋅t
The Attempt at a Solution
I...
Homework Statement
A car traveling at a constant speed of 24.0m/s passes a trooper hidden behind a billboard. One second after the speeding car passes the billboard, the trooper sets off in a chase with a constant acceleration of 3.0m/s^2.
A) How long does it take the trooper to overtake the...
Homework Statement
A turtle and a rabbit engage in a footrace over a distance of 4.00km. The rabbit runs 0.500km and then stops for a 90min nap. Upon awakening, he remembers the race and runs twice as fast. Finishing the course in a total time of 1.75h, the rabbit wins the race.
A) Calculate...
Homework Statement
A person riding a bike travels at an average velocity of 3m/s for 30min. The person then takes a water break for 15 min. The person finally travels a distance of 450m at an average velocity of 1.5m/s. What is the persons average velocity?
2. Homework Equations
[/B]
Average...
Homework Statement
A commercial claims that a car can stop on a dime (17.9mm). If a car is initially traveling at 13.4m/s, what acceleration would the car experience coming to a stop in that short distance?
Homework Equations
avg acceleration
Coversion
The Attempt at a Solution
I recognize...
Homework Statement
A ball is traveling at 3m/s then bounces off of a tennis racket and returns at 2m/s. If the ball is in contact with the racket for 12ms, what is the average acceleration?
Homework Equations
average acceleration and conversion
a=Vf-Vi/Tf-Ti
1s= 1000ms
The Attempt at a...
Homework Statement
A straight line is marked in meters in a field. A student begins at the zero position mark and ends at the 50 position mark. However, the student did not walk along the straight line. He uses a wheel that has a circumference of 1m and finds that it turns 100 times as he...
Homework Statement
Find the initial velocity v0x such that the particle will have the same x-coordinate at time t= 4.07 s as it had at t=0.
The acceleration of a particle is given by ax(t)=−2.00 m/s2 +( 3.09 m/s3 )t.
Homework Equations
v = v0 + a t
Δx = ((v+v0)/2)t
Δx = v0t + 1/2at^2
v^2 =...
Homework Statement
Homework Equations
$$h=ut+1/2at^2$$ $$h=x\tan\theta-1/2g\frac{x^2}{u^2\cos^2\theta}$$
The Attempt at a Solution
I tried to take a random angle theta for the lower particee and then using the equation of the upper particle tried to solve them together and find condition for...
Homework Statement
This problem showed up in my final review packet, and I /think/ it should be basic kinematics, but I don't even know how to approach it with the second half of it.
An object moves according to the equation x = vt + ke^(bt), where k, v, and b are constants, x represents...
Homework Statement
Object launched vertically with v initial =20 m/s. No air resistance. How long does it take to reach its max height?
Homework Equations
1/2 at^2 + vot = dy
.5mv^2=mgh
The Attempt at a Solution
I began by using conservation of energy to find the max height. .5mv^2 = mgh...
While doing some calculations on v_rms using the Maxwell-Boltzmann distribution, I noticed that v_rms and v_avg are pretty similar (https://casper.berkeley.edu/astrobaki/index.php/File:MaxwellSpeedDist.png).
In fact, really it's just the choice of using the 1-norm (|v|_avg) vs. 2-norm sqrt(v^2...
Homework Statement
You are at a stoplight when you see a car approaching from behind at constant velocity. To avoid getting rear-ended, you accelerate forward with constant acceleration. Assume that you have managed to start at the last possible instant to avoid getting hit, as determined by...
Homework Statement
A ball is dropped from the top of a 55.0 m -high cliff. At the same time, a carefully aimed stone is thrown straight up from the bottom of the cliff with a speed of 21.0 m/s . The stone and ball collide part way up.
How far above the base of the cliff does this happen...
Homework Statement
The directed beam from a small but powerful searchlight placed on the ground tracks a small plane flying horizontally at a fixed height h above the ground with a uniform velocity v. If the search light starts rotating with an instantaneous angular velocity ##\omega_0## at...
Homework Statement
This problem-solving question is about a police car chasing criminals.
Two cars are moving in the same direction, parallel (assumed).
One car is moving at 82 km/h.
The other car is moving at 64 km/h.
Bullets are fired from the car moving at 82 km/h towards the car moving at...
Homework Statement
At t = 0, one toy car is set rolling on a straight track with initial position 16.0 cm, initial velocity -3.7 cm/s, and constant acceleration 2.90 cm/s2. At the same moment, another toy car is set rolling on an adjacent track with initial position 10.0 cm, an initial velocity...
Homework Statement
"Derive the equations for position (in terms of acceleration, initial position, initial velocity, and time) and velocity (in terms of constant acceleration, a, initial velocity, v0, and time, t) from the definitions of position, velocity, and acceleration (derivative...
Homework Statement
Homework EquationsThe Attempt at a Solution
So (i) was easy enough and I got a time of 0.67 seconds.
For (ii), since the horizontal time is 0.67 seconds this means the TOTAL time spent in air is also 0.67 seconds, so to calculate max height we split this time in half...
Homework Statement
A pumpkin was dropped from a balcony of a skyscraper. The pumpkin happened to land on a sidewalk force sensor and the below data was collected. The pumpkin weighs 2.7kg.
a) From what height was the pumpkin dropped?
b) From what floor of the skyscraper was the...
Homework Statement
A falling stone takes 0.28 s to travel past a window 2.2 m tall.
From what height above the top of the window did the stone fall?
So from this problem I think I have these variables:
vo = ? (or 0 because falling usually indicates 0 for an initial velocity?)
yo = 0
y = 2.2m...
Why 's' in all kinematics equation is displacement.
S = Ut + ½a t^2 , v^2 = u^2 + 2aS
is it because S in v = dS/dt is a small distance , very small distance and we treat it as a position of particle at a time t1 during Δt→0 and its direction is from t1(intial position) to t2(final...
Homework Statement
While standing at the edge of the roof of a building, you throw a stone upward with an initial speed of 6.91 m/s. The stone subsequently falls to the ground, which is 16.5 m below the point where the stone leaves your hand. At what speed does the stone impact the ground? How...
Homework Statement
Two baseballs are set in motion from the top of a 5 m tall tower. One is thrown straight down toward the ground with an initial velocity of 20 m/s. The second is thrown straight up toward the sky with an initial velocity of 20 m/s.
How do their velocities compare when they...
Homework Statement
Ok I have the answers to parts a and b, which I am 100% confident in since they are simple computations
Question is in attachement
a)74.9 rad/s
b)168.08 rad
My issue comes in when I have to get parts c
The mass of the cylinder is 8.7kg,
its diameter is .18m,
its .35m long...
Homework Statement
Two points P and Q move in a straight line AB.The point P starts from A in the direction AB with velocity and acceleration http://latex.artofproblemsolving.com/b/b/2/bb2c93730dbb48558bb3c4738c956c4e8f816437.png.At the same instant of time Q starts from B in the direction of...
x = x0 + v0 * t + 1/2 * constant acceleration * t^2
So this is supposed to be very very simple physics, but I still feel like there's a part of this equation I don't fully understand. The first term is the initial position of the body at t=0. The second term is the initial velocity at t=0...
Homework Statement
Homework Equations
relevant equations are listed with each question
The Attempt at a Solution
25. **
Displacement = 131 km (South)
Average velocity = total displacement / total time
Average velocity = 131 km (S) / 2.0 h
Average velocity = 65.5 km /h (south)
26. **...