Aconcrete pump of 120-cy/hr max. output is used to place 250 cy of concrete. it is supplied by 8 cy transit-mix trucks arriving to the site every 15 mins. barring interruptions how many hours will the operation require, considering 80% efficiency factor?
the correct answer is a. lever
from all the choices available in that question, it's closest in size to the dot over the ' i ' in the words "radius", "is" and "in".
“without loss of generality, we only need to look at the equation for the x-position, since we know that centripetal acceleration points towards the center of the circle. thus, when θ = 0, the second derivative of x with respect to time must be the centripetal acceleration.
the first derivative of x with respect to time t is:
dx/dt = —rsinθ(dθ/dt)
the second derivative of x with respect to time t is:
d2x/dt2 = —rcosθ(dθ/dt)2—rsinθ(d2θ/dt2)
in both of the above equations the chain rule of calculus is used and by assumption θ is a function of time. therefore, θ can be differentiated with respect to time.
now, evaluate the second derivative at θ = 0.
d2x/dt2 = —r(dθ/dt)2
the term dθ/dt is usually called the angular velocity, which is the rate of change of the angle θ. it has units of radians/second.
for convenience we can set w ≡ dθ/dt.
d2x/dt2 = —rw2
this is the well-known form for the centripetal acceleration equation.”