Complete Question
A 100-W (watt) light bulb has resistance R=143Ω (ohms) when attached to household current, where voltage varies as V=V0sin(2πft), where V0=110 V, f=60 Hz. The power supplied to the bulb is P=V2R J/s (joules per second) and the total energy expended over a time period [0,T] (in seconds) is
Compute U if the bulb remains on for 5h
Answer:
The value is
Explanation:
From the question we are told that
The power rating of the bulb is
The resistance is
The voltage is
The energy expanded is
The voltage
The frequency is
The time considered is
Generally power is mathematically represented as
=>
=>
So
=>
=>
=>
=>
=>
=>
Circumference C=2πr
<span>C=2π(1.5x10^8)=9.42x10^8 </span>
<span>In 365 Days there are 8760hr </span>
<span>V=distance/time </span>
<span>V=(9.42x10^8)/8760=107534.2km/hr </span>
(a) 5.66 m/s
The flow rate of the water in the pipe is given by
where
Q is the flow rate
A is the cross-sectional area of the pipe
v is the speed of the water
Here we have
the radius of the pipe is
r = 0.260 m
So the cross-sectional area is
So we can re-arrange the equation to find the speed of the water:
(b) 0.326 m
The flow rate along the pipe is conserved, so we can write:
where we have
and where is the cross-sectional area of the pipe at the second point.
Solving for A2,
And finally we can find the radius of the pipe at that point:
The change in angular displacement as a function of time is the definition given for angular velocity, this is mathematically described as
Here,
= Angular displacement
t = time
The angular velocity is given as
PART A) The angular velocity in SI Units will be,
PART B) From our first equation we can rearrange to find the angular displacement then
Replacing,