The two-member frame (see picture attached) supports the 200-lb cylinder and 500
lb–ft couple moment. Determine the force of the roller at B on member
AC and the horizontal and vertical components of force which the pin at
C exerts on member CB and the pin at A exerts...
im just not sure if this means that its -6.216i for the position vector of AD or -6.216i for the actual x component for the tensile force...I just don't see how it could be -6.216 for the tensile force when the magnitude is 14000 lbs.
Having the x component of the position vector of AD...
For cable AD it is known that the magnitude is 14 kips, x-component has a value of -6.216, the direction angle in the z-direction is 83.63°, and Fy is less than zero. Find forces in Cartesian vector form, coordinates of point D if it lies on the x-z plane and point A is (0...
If F_1 = 100N , F_2 = 120N and F_3 = 80N , determine the magnitude and coordinate direction angles of the resultant couple moment.
M=r x F
MR=Ʃ(r x F)
The Attempt at a Solution
I found the couple moment for each force:
the force of the spring is k(s)... k=600 is given, and I know s = l - l0; therefore Fspring=600(l-l0).
l0 is also given and equals 1.5m so the equation becomes 600(l - 1.5). Looking at the triangle the two springs create with the wall we can deduce that l (length of the stretched spring) is...
The springs AB and BC have stiffness k and an unstretched length of l. Determine the
displacement d of the cord from the wall when a force F is applied to the cord. See Picture attached.
l = 3 m
k = 600 N/m
F = 200 N
a) Express each force as a Cartesian vector.
b) Determine the magnitude and coordinate direction angles of the resultant force acting on the hook.
See figured attached.
The Attempt at a Solution
First I expressed F1 and F2 into its x, y...
A mathematical model for temperature T as a function of depth y (in m) and time t (in days) is:
where Tsurf(t) is the water temperature of the lake surface at time t, α is a property called the “eddy thermal diffusivity” and...
so for the second partial I get:
and the second part asks me to get the partial of this with respect to "t"... when doing this does Tsurf(t) just becomes T'surf(t)?
oh wow yeah...
so the first derivative would come out to (Tsurf(t)-T0)e^(-y2/4αt)(-2y/4αt) which then simplifies to (-y/2αt)(Tsurf(t)-T0)e^(-y2/4αt), correct?
And then for the second derivate I would need to product rule this all up...
The separation of layers is considered to occur at the thermocline, which is defined as the location of the steepest slope in the temperature gradient. Mathematically, this occurs at the inflection point – so the position of the thermocline can be found from the following...
from T(y,t)=e^(-y2/4αt)(Tsurf(t)-T0)+T0 I know that only the exponential expression contains a y so everything else becomes a constant and the last T0 drops off...
so for the first partial derivative this becomes (Tsurf(t)-T0)e^(-y2/4αt)(-2/4αt)
then for the second partial its pretty much...
Lakes become stratified in temperature over the course of the year because of the way that heat transfer occurs. In the spring, the temperature of a lake as a function of depth is reasonably constant. During the summer, as heat enters the lake from solar radiation, the...