thats the thing i know how to integrate ln(x) where x is any function wih power 1.
ln(x^3-1)
let t = x^3-1 --> 3x^2dx=dt when i sub that in i dont know how to proceed
=ln(t)dt/3x^2 --> maybe another substitution, ie let u=3x^2, du=6xdt,
any help guys?
Homework Statement
Integral of: 2x^3/(x^3-1) with respect to x.
The Attempt at a Solution
you can divide them to get sum of integrals.
=int(2,x) + 2*int(1/(x^-1),x)
=2x + 2*int(1/(x^-1),x)
Im having trouble proceeding with the last part, i just need help getting started.
but since it is a varying force, how would i use the scalar product, it isnt a constant force. should i only apply it to the final position where. what is the formula for Wa? since its the negative of Wg= mghcos180=-(9.8)(170)(0.86)=-1429 J. Wa should be +1429J but how can i calculate it...
Wa is the work done by the applied force.
since at any point on the rope it is right angles to displacement cos90=0 so then tcos90=0. the answer in the book is 0 too.
thats what i think.
so for a, are the calculations correct? tension will have its corresponding components, yes.
and for c work due to tension is always 0 then (cos90)
"why isn't the component of Force along x = M*g*Sinθ" how did you come to that conclusion???
EDIT: how would one calculate the Wa without setting...
for (a) gravity does not have any components. i think you misread the question. ive attached a diagram.
for (b) since the change in kinetic energy is zero, mgh is equal to the negative of work
for (c) i dont quite understand
given/known data
A 170 kg crate hangs from end of rope length L = 15 m. You push horizontally on crate with varying force F to move distance d = 5 m sideways. (a) What magnitude be of F when crate is in final position? During crate's displacement, what are (b) the total work done on it, and (c)...
[SOLVED] Solubility Thallous Chloride
Homework Statement
6.5g of thallous chloride is added to 750ml of water at room temperature to determine Ksp. The solution is stirred from time to time over a 4h period. Some thallous chloride does not dissolve and the solution is declared saturated. A...
Homework Statement
Find all values of t so that the three vectors a=(1,2,3) b=(4,5,6) and c=(7,8,t) are coplanar.
Homework Equations
(axb) \bullet c=0
The Attempt at a Solution
(1, 2, 3) x (4, 5, 6)
(-3,6,-3)
(-3,6,-3)\bullet(7,8,t)
27=3t
t=9
it says find ALL values of t. i keep getting 9...
Homework Statement
300 kg speedboat is pulling two 25 kg skiers using ropes. Each rope makes an angle of 30 with the boat axis. Each rope exerts 500N force and acc. is 2m/s^2. What force must the boat exert on water to keep skiers moving?
Homework Equations
a=Fnet/m
The Attempt at a...
I think I understand most of what you are saying, however I am not trying to go from rectangular to polar, I just want to verify this in rectangular form.
I'm sorry I do not understand. Please simplify the sentence.
There is a question asking to find and verify parametric equations for an ellipse. How would we start and finish such a complex question? Thank you in advance.
Homework Statement
Find and verify parametric equations for an ellipse.
Homework Equations
x=acost
y=bsint
The Attempt at a Solution
lets say the equation is x=3cost, y=3sint, domain: 0 to 2pi
x2 y2
-- + -- = 1
a2 b2
point does verify when t=0 x=3, y=0 which =1...
[SOLVED] Newtons Second Law
Homework Statement
On a force/mass vs acceleration graph where force/mass is horizontal, what does the slope represent?
Homework Equations
The Attempt at a Solution
My calclations: ex. (2m/s^2 - 1m/s^2)/(3 N/kg - 1N/kg)
=.5 (m/s^2)/(N/kg)...
[SOLVED] The Flea
Homework Statement
A flea, jumping with its highest possible initial speed, can jump to a maximum vertical height of 1 cm. What is
the time spent in the air by the flea during the vertical jump? What would be the time spent in the air if the flea
were instead to leave the...