Answer:
E = 31.329 N/C.
Explanation:
The differential electric field
at the center of curvature of the arc is
<em>(we have a cosine because vertical components cancel, leaving only horizontal cosine components of E. )</em>
where
is the radius of curvature.
Now
,
where
is the charge per unit length, and it has the value

Thus, the electric field at the center of the curvature of the arc is:


Now, we find
and
. To do this we ask ourselves what fraction is the arc length 3.0 of the circumference of the circle:

and this is
radians.
Therefore,

evaluating the integral, and putting in the numerical values we get:


Answer:
a)
= 928 J
, b)U = -62.7 J
, c) K = 0
, d) Y = 11.0367 m, e) v = 15.23 m / s
Explanation:
To solve this exercise we will use the concepts of mechanical energy.
a) The elastic potential energy is
= ½ k x²
= ½ 2900 0.80²
= 928 J
b) place the origin at the point of the uncompressed spring, the spider's potential energy
U = m h and
U = 8 9.8 (-0.80)
U = -62.7 J
c) Before releasing the spring the spider is still, so its true speed and therefore the kinetic energy also
K = ½ m v²
K = 0
d) write the energy at two points, maximum compression and maximum height
Em₀ = ke = ½ m x²
= mg y
Emo = 
½ k x² = m g y
y = ½ k x² / m g
y = ½ 2900 0.8² / (8 9.8)
y = 11.8367 m
As zero was placed for the spring without stretching the height from that reference is
Y = y- 0.80
Y = 11.8367 -0.80
Y = 11.0367 m
Bonus
Energy for maximum compression and uncompressed spring
Emo = ½ k x² = 928 J
= ½ m v²
Emo =
Emo = ½ m v²
v =√ 2Emo / m
v = √ (2 928/8)
v = 15.23 m / s
Answer:
Y component = 32.37
Explanation:
Given:
Angle of projection of the rocket is, 
Initial velocity of the rocket is, 
A vector at an angle
with the horizontal can be resolved into mutually perpendicular components; one along the horizontal direction and the other along the vertical direction.
If a vector 'A' makes angle
with the horizontal, then the horizontal and vertical components are given as:

Here, as the velocity is a vector quantity and makes an angle of 33.6 with the horizontal, its Y component is given as:

Plug in the given values and solve for
. This gives,

Therefore, the Y component of initial velocity is 32.37.
Answer:
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