Answer:
The compression is .
Explanation:
A Hooke's law spring compressed has a potential energy
where k is the spring constant and the distance to the equilibrium position.
A mass m moving at speed v has a kinetic energy
.
So, in the first part of the problem, the spring is compressed a distance d, and then launch the mass at velocity . Knowing that the energy is constant.
If we want to double the kinetic energy, then, the knew kinetic energy for a obtained by compressing the spring a distance D, implies:
But, in the left side we can use the previous equation to obtain:
And this is the compression we are looking for
The whole secret of things that are balanced on a pivot like this is:
The sum of all of the 'moments' is equal on both sides.
The moment of each weight is (the weight) times (its distance from the pivot).
If you add up those for each eight on one side, it has to be equal to the sum
of all the ones on the other side.
<u>2. a).</u>
The moments on the right side are: (4 x 0.15) and (1 x 0.40).
They add up to (0.60 + 0.40) = 1.00
The only moment on the left side is (C x 0.25). Both sides have to be equal.
C x 0.25 = 1.00
Divide each side by 0.25, and you have C = 4 N .
===========================================
<u>2. b).</u>
The only moment on the left side is (5 x 0.40) = 2.00
The moments on the right side are (1 x 0.20) and (D x 0.30)
They add up to (0.3D + 0.2).
Both sides have to be equal. 0.3D + 0.2 = 2.0
Subtract 0.2 from each side: 0.3D = 1.8
Divide each side by 0.3: D = 6 N
Answer:
The standard deviation of corrected pH is
5.64 , 1.32
Explanation:
To find the measurements pH given
μx = 4.60 , σx = 1.10
So using the measurement as a pH
μₐX + b = aμ X + b
μ1.2 x + 0.12
1.2 (4.60) + 0.12 = 5.64
σₐX +b = a σ X
σ 1.2 X + 0.12
1.2 (1.10) = 1.32
Answer:
Monitoring water quality is an important part of helping us determine whether or not we are making progress in cleaning up our waterways. It reveals the health and composition of streams, rivers, and lakes at a snapshot in time, as well as over weeks, months, and years. Dirty water could be dangerous to us, and our environment!