Homework Statement
For the case of a strong shock propagating into a gas with \gamma=7/5 What is the ratio \rho2/\rho1
Homework Equations
\rho\ u=constant
P+ \rho\ u^2=constant
\frac{1}{2} u+ \frac{\gamma }{\gamma -1}\frac{\ P}{\rho} = constant
The Attempt at a Solution
I can use the 3...
Homework Statement
A boat is to dock with a ship. The ship sails along a straight course with speed v. The boat moves with constant speed nv, its motion always being always directed towards the ship. Show that the polar equation of the course of the boat as observed from the ship is...
I've been told by my teacher that we are supposed to use the fundamental theorem of calculus for part c
so for part b I define the indefinite integral as
$\ F(x) = \int_a^x f(t)dt = F(x) - F(a) = F(x) +C
and for part c
I take $\int_x^{x+h} f(t) dt = F(x+h) - F(x) \approx f(x)h...
I think I'm ok with part a and b now but my textbook doesn't have the fundamental theorem of calculus in it. I have looked on the internet but all of the proofs for part c give the integral limits and an indefinite integral doesn't have limits.
for a my guess is something like...
Homework Statement
a) Write down the definition of the definite integral in terms of a limiting procedure of elementary areas
b) Write down the definition of the indefinate integral
c) Show that the derivative of an indefinite integral of f(x) is f(x)
The Attempt at a Solution...
thanks for the reply. ok, i think i get what you are saying.
we have resolving vertically: \ Mg = N_A + N_B (1)
and taking moments clockwise about the centre of mass
\ Mah + \frac{N_{A}L}{2} = \frac{N_{B}L}{2} (2)
If I approximate \frac{L}{2} = h because the feet are small...
Homework Statement
A cubical block of mass \ M and side length \ L with small feet attached to the 4 corners of its base is placed on a rough conveyer belt initially at rest. The centre of mass of the box is midway between the front and rear feet and is a height \ h above the belt. The...