Answer:
a) dh/dt = -44.56*10⁻⁴ cm/s
b) dr/dt = -17.82*10⁻⁴ cm/s
Explanation:
Given:
Q = dV/dt = -35 cm³/s
R = 1.00 m
H = 2.50 m
if h = 125 cm
a) dh/dt = ?
b) dr/dt = ?
We know that
V = π*r²*h/3
and
tan ∅ = H/R = 2.5m / 1m = 2.5 ⇒ h/r = 2.5
⇒ h = (5/2)*r
⇒ r = (2/5)*h
If we apply
Q = dV/dt = -35 = d(π*r²*h/3)*dt
⇒ d(r²*h)/dt = 3*35/π = 105/π ⇒ d(r²*h)/dt = -105/π
a) if r = (2/5)*h
⇒ d(r²*h)/dt = d(((2/5)*h)²*h)/dt = (4/25)*d(h³)/dt = -105/π
⇒ (4/25)(3*h²)(dh/dt) = -105/π
⇒ dh/dt = -875/(4π*h²)
b) if h = (5/2)*r
Q = dV/dt = -35 = d(π*r²*h/3)*dt
⇒ d(r²*h)/dt = d(r²*(5/2)*r)/dt = (5/2)*d(r³)/dt = -105/π
⇒ (5/2)*(3*r²)(dr/dt) = -105/π
⇒ dr/dt = -14/(π*r²)
Now, using h = 125 cm
dh/dt = -875/(4π*h²) = -875/(4π*(125)²)
⇒ dh/dt = -44.56*10⁻⁴ cm/s
then
h = 125 cm ⇒ r = (2/5)*h = (2/5)*(125 cm)
⇒ r = 50 cm
⇒ dr/dt = -14/(π*r²) = - 14/(π*(50)²)
⇒ dr/dt = -17.82*10⁻⁴ cm/s
Answer: the loop will move up
Explanation:
Whenever an electric current cuts across magnetic field lines, a force is exerted on the current - carrying conductor
According to Fleming's left hand rule, the thumb is the direction of motion.
First finger is the direction of magnetic field, while the second finger is the direction of the conventional current.
When a current flow in the will, the wire will experience an upward force. And continue to rotate in an up - down direction. Therefore, the loop will move up.
Answer:
1.24 m/s
Explanation:
Metric unit conversion:
9.25 mm = 0.00925 m
5 mm = 0.005 m
The volume rate that flow through the single pipe is
This volume rate should be constant and divided into the 4 narrower pipes, each of them would have a volume rate of
So the flow speed of each of the narrower pipe is:
Answer:
a) m_ttoal = 40x
, b) m_total = 100X
, c) m_total = 400X
,
d) m_total = 1000 X
Explanation:
La magnificación o aumentos es el incremento de del tamaño de la imagen con respecto al tamaño original del objeto, en la mayoria del os sistema optico la magnificacion total es el producoto de la magnificación del objetivo por la magnificación del ocular
m_total = m_ objetivo * m=ocular
apliquemos esto a nuestro caso
1) m_total = 4 x * 10 x
m_ttoal = 40x
2) m_total = 10X * 10X
m_total = 100X
3)mtotal = 40X * 10X
m_total = 400X
4) m _totla = 100x * 10 X
m_total = 1000 X
en este ultimo caso para magnificación grandes es decalcificar el objeto
