Finding the Length of a Curve: Step-by-Step Guide

  • Thread starter Thread starter mugzieee
  • Start date Start date
  • Tags Tags
    Curve Lenght
AI Thread Summary
To find the length of the curve defined by the parametric equations x=sqrt(5)sin2t -2 and y=sqrt(5)cos2t - sqrt(3), start by determining the values of t for the desired interval. The arc length formula for a parameterized curve is given by the integral of the square root of the sum of the squares of the derivatives of x and y with respect to t. Specifically, the formula is CurveLength_{t=a}^{t=b} = ∫_{a}^{b} √((dy/dt)² + (dx/dt)²) dt. It is noted that if approached correctly, the problem can be simplified significantly. Understanding the limits of integration is crucial for solving the integral.
mugzieee
Messages
77
Reaction score
0
i got a problem that says:
x=sqrt(5)sin2t -2
y=sqrt(5)cos2t - sqrt(3)

how would i go about starting it?
 
Physics news on Phys.org
Do you know the equation for arc length for a parameterized curve?

--J
 
One other thing:You may want to know between which points you wish to compute the length...?In other words,give 2 distinct values of "t"...The integral doesn't seem to be difficult...

Daniel.
 
mugzieee said:
i got a problem that says:
x=sqrt(5)sin2t -2
y=sqrt(5)cos2t - sqrt(3)

how would i go about starting it?
:(1): \ \ \ \ (CurveLength_{t=a}^{t=b}) = \int_{a}^{b} \sqrt { (\frac {dy} {dt})^2 + (\frac {dx} {dt})^2} \ \ dt

(HINT: If solved correctly, this problem simplifies very rapidly!)


~~
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Are the 2nd and 3rd problems in this video correctly solved? (charged dipole and organ pipe problems)
Replies
3
Views
965
How to correctly round in physics?
Replies
8
Views
2K
Find speed of CoM after collision between ball and "square structure"
Replies
42
Views
3K
Solving a Partial Derivative Problem Step-by-Step
Replies
5
Views
1K
Understanding a math step in solving Schrödinger's equation for single particle in a box
Replies
8
Views
857
Where on a rigid body is a resultant force applied?
Replies
11
Views
1K
Finding the shape of a hanging rope
Replies
3
Views
697
Finding the magnitude (length) and direction (angle) of a vector
Replies
2
Views
1K
Find the step on which the hockey puck will land
Replies
6
Views
1K
Quantum Mechanics I, finding impuls wavefunction.
Replies
6
Views
875

Hot Threads

Recent Insights

Back
Top