Answer:
180,000
Explanation:
Frequency is a quantity that is measured in Hertz [Hz] and it represents the number of rotations per second.
A motor with a frequency of 50 Hz will rotate 50 times per second.
Since we don't want to know how many times it rotates per second, but per hour. The first step is to find how many seconds there are in an hour and then multiply that amount by 50.
Seconds in an hour:
there are 60 seconds per minute, and 60 minutes per hour, thus there are
60*60 = <u>3,600 seconds in an hour</u>
We know that the motor will rotate 50 times per second so to find the number of rotations in 1 hour = 3,600 seconds we multiply:
50*3,600 = 180,000 rotations
Answer:
(a) 17634.24 Ω
(b) 0.0068 A
Explanation:
(a)
The formula for inductive inductance is given as
X' = 2πFL................... Equation 1
Where X' = inductive reactance, F = frequency, L = inductance
Given: F = 60 Hz, L = 46.8 H, π = 3.14
Substitute into equation 1
X' = 2(3.14)(60)(46.8)
X' = 17634.24 Ω
(b)
From Ohm's law,
Vrms = X'Irms
Where Vrms = Rms Voltage, Irms = rms Current.
make Irms the subject of the equation
Irms = Vrms/X'...................... Equation 2
Given: Vrms = 120 V, X' = 17634.24 Ω
Substitute into equation 2
Irms = 120/17634.24
Irms = 0.0068 A
Relative to the positive horizontal axis, rope 1 makes an angle of 90 + 20 = 110 degrees, while rope 2 makes an angle of 90 - 30 = 60 degrees.
By Newton's second law,
- the net horizontal force acting on the beam is

where
are the magnitudes of the tensions in ropes 1 and 2, respectively;
- the net vertical force acting on the beam is

where
and
.
Eliminating
, we have





Solve for
.


