Answer:
- <u>C = Q/∆V . So the overall strategy here is to find the potential difference ∆V corresponding to a particular Q on an object, then take the ratio.</u>
Explanation:
Capacitance is the amount of charge something can hold for a given ap- plied potential difference between separated parts of the conductor:
You can just use basic
trigonometry to solve for the x & y components.
<span>vector a = 10cos(30) i +
10sin(30) j = <5sqrt(3), 5></span>
vector b is only slightly harder because the angle is relative
to vector a, and not the positive x-axis. Anyway, this just makes vector b with
an angle of 135deg to the positive x-axis.
<span>vector b = 10cos(135) i +
10sin(135) j = <-5sqrt(2), 5sqrt(2)></span>
So
now we can do the questions:
r = a + b
r = <5sqrt(3)-5sqrt(2), 5+5sqrt(2)>
(a)
5sqrt(3)-5sqrt(2)
(b)
5+5sqrt(2)
(c)
|r|
= sqrt( (5sqrt(3)-5sqrt(2))2 + (5+5sqrt(2))2 )
=
12.175
(d)
θ = tan-1 (
(5+5sqrt(2)) / (5sqrt(3)-5sqrt(2)) )
θ
= 82.5deg
<span> </span>
Answer:
u" + 40u' + 49u = 2 sin(t/6)
upp + 40up + 49u = 2 sin(t/6)
Explanation:
Step 1: Data given
mass = 5 kg
L = 20 cm = 0.2 m
F = 10 sin(t/6)N
Fd(t) = - 6 N
u(0) = 0.03 m/s
u(0) = 0
u'(0) = 3 cm/s
Step 2:
ω =kL
k = ω/L = m*g /L = (5*9.8)/0.2 = 245 kg/s²
Since Fd(t) = -γu'(t) we know:
γ =- Fd(t) / u'(t) = 6N/ 0.03 m/s = 200 Ns/m
The initial value problem which describes the motion of the mass is given by
5u" + 200u' + 245u = 10 sin(t/6) u(0) = 0 ; u'(0) = 0.03
This is equivalent to:
u" + 40u' + 49u = 2 sin(t/6) u(0) = 0 ; u'(0) = 0.03
upp + 40up + 49u = 2 sin(t/6)
With u in m and t in s
Answer:
5.72 s
Explanation:
From Newton's law, F = ma
The East is +ve direction, Hence,
F = +8930 N
m = 2290 kg
a = ?
8930 = 2290 × a
a = 8930/2290 = 3.90 m/s²
So, we will find the time it takes the car to stop using the equations of motion
a = 3.90 m/s²
u = initial velocity of the car = - 22.3 m/s (the velocity is to the west)
v = final velocity of the car = 0 m/s (since the car comes to rest)
t = time taken for the car to come to rest = ?
v = u + at
0 = - 22.3 + (3.90)(t)
3.9t = 22.3
t = 5.72 s
Answer:
What are we supposed to find, if it is kinetic energy then this is the solution.
K.E=1/2mv^2
K.E= kinetic energy
M=mass
V=velocity
K.E =0.5*55*0.6^2
K.E=9.9J
Explanation:
