Use differential calculus to find the maximum/minimum for an
engineering problem.
A sheet of metal is 340 mm x 225 mm and has four equal squares
cut out at the corners so that the sides and edges can be turned up
to form an open topped box shape.
Calculate: (a) The lengths of the sides of the cut-out squares
for the volume of the box to be as big as possible.
(b) The maximum volume of the box.
A metal cylinder with a mass of 3.50 kg is attached to a spring
and is able to oscillate horizontally with negligible friction. The
cylinder is pulled to a distance of 0.200 m from its equilibrium
position, held in place with a force of 18.0 N,and then released
from rest. It then oscillates in simple harmonic motion. (The
cylinder oscillates along the x-axis, where
x = 0
is the equilibrium position.)
(a)
What is the spring constant (in N/m)?
N/m...
Blackwater Spring and Metal utilizes the same computerized
spring-forming machinery in its U.S. and Malaysian plants. The
first cost was $750,000 with S = $150,000 after n = 10 years. MACRS
(Modified Accelerated Cost Recovery System) depreciation with n = 5
years is applied in the United States, and standard SL depreciation
with n = 10 years is used by the Malaysian facility. If the
equipment is sold after 6 years for $100,000, calculate the
over-and underdepreciation amounts for each...
Blackwater Spring and Metal utilizes the same computerized
spring-forming machinery in its U.S. and Malaysian plants. The
first cost was $750,000 with S = $150,000 after n
= 10 years. MACRS (Modified Accelerated Cost Recovery System)
depreciation with n = 5 years is applied in the United
States, and standard SL depreciation with n = 10 years is
used by the Malaysian facility.
If the equipment is sold after 6 years for $100,000, calculate
the over-and underdepreciation amounts for each...
You have a vertical metal rod, a spring with one end closed and
the other end open so that it can slide down over the rod and then
fly up when released, and a meter stick. The mass of the spring is
15g and its spring constant k is 6 N/m Your group decides to test
the work-energy principle by stretching the spring a distance Dy =
30 cm, releasing it from rest and measuring how high it goes. Use...