Answer:
See the answers below.
Explanation:
The total power of the circuit is equal to the sum of the powers of each lamp.
Now we have a voltage source equal to 240 [V], so by means of the following equation we can find the current circulating in the circuit.
where:
P = power [W]
V = voltage [V]
I = current [amp]
So this is the answer for c) I = 0.67 [amp]
We know that the voltage of each lamp is 240 [V]. Therefore using ohm's law which is equal to the product of resistance by current we can find the voltage of each lamp.
a)
where:
V = voltage [V]
I = current [amp]
R = resistance [ohms]
Therefore we replace this equation in the first to have the current as a function of the resistance and not the voltage.
b)
The effective resistance of a series circuit is equal to the sum of the resistors connected in series.
Answer:
Explanation:
spring constant of spring = mg / x
= .4 x 9.8 / ( .95 - .65 )
=13.07 N / m
energy stored in spring = 1/2 k x²
= .5 x 13.07 x ( 1.2 - .65 )²
= 1.976 J
Let it goes x m beyond its equilibrium position
Total energy at initial point
= 1.976 + 1/2 m v²
= 1.976 + .5 x .4 x 1.6²
= 2.488 J
energy at final point
= mgh + 1/2 k x²
.4 x 9.8 x ( .55 + x ) + .5 x 13.07 x² = 2.488
6.535 x² + 2.156 + 3.92 x = 2.488
6.535 x² + 3.92 x - .332 = 0
x = .075 m
7.5 cm
Answer:
a) 2.53 * 10^-2 m/s
b) -4.78 * 10^-2 m/s
c) 1.21 * 10^-1 m/s
Explanation:
Given data :
Mass of block = 10 kg
Measuring 250mm on each side
a) calculate the speed when a force of 75N is applied to pull block upwards
F = f + W sin∅ ( equation for applying the force of equilibrium condition in the x axis ) ----- ( 1 )
f ( friction force )= ( 16400v * 6.25 *10^-2) = 1025 v
F ( force applied ) = 75
W ( weight of block ) = 10 * 9.81 = 98.1 N
∅ = 30°
input values into equation 1
V = = 2.53 * 10^-2 m/s
b) Speed when no force is applied on the block
F = f + W sin∅
F = 0
f = 1025 V
W = 98.1 N
∅ = 30°
hence V = = - 4.78 * 10^-2 m/s
c) when a force is applied to push block down the incline
F = f + W sin∅ ----- ( 3 )
F = 75 N
f = 1025 V
W = 98.1 N
∅ = 30°
input values into equation 3 considering the fact that the weight of the block is acting in the opposite direction
75 = 1025 V - 98.1 ( sin 30° )
V = = 1.21 * 10^-1 m/s
The electric field due to a point charge of 20uC at a distance of 1 meter away from it is 180000 .
First, you have to know that the space surrounding a load suffers some kind of disturbance, since a load located in that space will suffer a force. The disturbance that this charge creates around it is called an electric field.
In other words, an electric field exists in a certain region of space if, when introducing a charge called witness charge or test charge, it undergoes the action of an electric force.
The electric field E created by the point charge q at any point P, located at a distance r, is defined as:
where K is the constant of Coulomb's law.
In this case, you know:
- K= 9×10⁹
- q= 20 uC=20×10⁻⁶ C
- r= 1 m
Replacing in the definition of electric field:
Solving:
<u><em>E=180000 </em></u><u><em /></u>
Finally, the electric field due to a point charge of 20uC at a distance of 1 meter away from it is 180000 .
Learn more:
Answer:
We know that the length is 79 (there are no units of length in the question, so i will leave it as it is written, without units) when the temperature is 2°C.
We want to find the increase in length when the temperature is 35°C, knowing that the linear expansion coefficient is 11*10^(-6) °C^-1
The change in length is just given by the equation:
where:
α = 11*10^(-6) °C^-1
T₀ is the initial temperature, so T₀ = 2°C
T₁ is the final temperature, so T₁ = 35°C
L₀ is the initial length, so L₀ = 79
Replacing these in the equation we get:
ΔL = ( 11*10^(-6) °C^-1)*79*(35°C - 2°C)
= 0.28677
So the length of the railroad will increase by 0.28677