Explanation:
Equilibrium position in y direction:
W = Fb (Weight of the block is equal to buoyant force)
m*g = V*p*g
V under water = A*h
hence,
m = A*h*p
Using Newton 2nd Law
Hence, T time period
T = 2*pi*sqrt ( h / g )
An empty office chair is at rest on a floor. Consider the following forces:. 1. A downward force due to gravity;. 2. An upward forc
1 answer:
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Answer:
(a) 1.939 m/h
(b) 0.926 m/h
(c) -0.315 m/h
(d) -1.21 m/h
Explanation:
Here, we have the water depth given by the function of time;
D(t) = 7 + 5·cos[0.503(t-6.75)]
Therefore, to find the velocity of the depth displacement with time, we differentiate the given expression with respect to time as follows;
D'(t) =
= 5×(-sin(0.503(t-6.75))×0.503
= -2.515×(-sin(0.503(t-6.75))
= -2.515×(-sin(0.503×t-3.395))
Therefore we have;
(a) at 5:00 AM = 5 - 0:00 = 5
D'(5) = -2.515×(-sin(0.503×5-3.395)) = 1.939 m/h
(b) at 6:00 AM = 6 - 0:00 = 6
D'(5) = -2.515×(-sin(0.503×6-3.395)) = 0.926 m/h
(c) at 7:00 AM = 7 - 0:00 = 7
D'(5) = -2.515×(-sin(0.503×7-3.395)) = -0.315 m/h
(d) at Noon 12:00 PM = 12 - 0:00 = 12
D'(5) = -2.515×(-sin(0.503×12-3.395)) = -1.21 m/h.
Answer:
A) 1000 joules
Explanation:
In general work is given by the equation:
(1)
A) With the displacement and
the force applied, because the force and the displacement are parallel (the crate is pushed horizontally)
is simply
, and because the path is a straight line and the force is constant work is:
(2),
B) The work-energy theorem says that the total work on a body is equal to the change on kinetic energy:
(3)
The total work on the crate is the work done by the push and plus the work of the friction (4) , as (A) because forces are parallel to the displacement
(5) and
(6), the due friction always has negative sign because is opposite to the displacement, using (6), (5) and (4) on (3):
(3)
C) The energy is lost by friction, so the amount of energy turned into heat is the work the friction does:
(3)