Please help, it's grade 7 science. :)
2 answers:
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A mass weighing 32 pounds stretches a spring 2 feet.
(a) Determine the amplitude and period of motion if the mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of 6 ft/s.
(b) How many complete cycles will the mass have completed at the end of 4 seconds?
Answer:
Period = seconds
8 cycles
Explanation:
A mass weighing 32 pounds stretches a spring 2 feet;
it implies that the mass (m) =
m=
= 1 slug
Also from Hooke's Law
2 k = 32
k =
k = 16 lb/ft
Using the function:
(because of the initial position being above the equilibrium position)
( as a result of upward velocity)
NOW, we have:
However;
means
also implies that:
Hence,
Period can be calculated as follows:
=
= seconds
How many complete cycles will the mass have completed at the end of 4 seconds?
At the end of 4 seconds, we have:
cycles
Answer:
The answer is 1.87nm/s.
Explanation:
The water loss must be replaced by
of sap. 110g of sap corresponds to a volume of
thus rate of sap replacement is
The volume of sap in the vessel of length is
,
where is the cross sectional area of the vessel.
For 2000 such vessels, the volume is
taking the derivative of both sides we get:
on the left-hand-side is the velocity
of the sap, and on right-hand-side
; therefore,
and since the cross-sectional area is
;
therefore,
solving for we get:
which is the upward speed of the sap in each vessel.