Answer:
M g H = 1/2 M v^2 potential energy = kinetic energy
v^2 = 2 g H = 2 * 9.80 * 6 = 117.6 m/s^2
v = 10.8 m/s
(C)
Answer:
<em>a) 0.72 V</em>
<em>b) 19.2 mA</em>
<em>c) 2.304 Watts</em>
Explanation:
A transformer is used to step-up or step-down voltage and current. It uses the principle of electromagnetic induction. When the primary coil is greater than the secondary coil, the it is a step-down transformer, and when the primary coil is less than the secondary coil, the it is a step-up transformer.
number of primary turns = 
= 500 turns
input voltage = 
= 120 V
number of secondary turns = 
= 3 turns
output voltage = 
= ?
using the equation for a transformer
substituting values, we have
= 360/500 =<em> 0.72 V</em>
<em></em>
b) by law of energy conservation,
where
= input current = ?
= output voltage = 3.2 A
= output voltage = 0.72 V
= input voltage = 120 V
substituting values, we have
120 = 3.2 x 0.72
120 = 2.304
= 2.304/120 = 0.0192 A
= <em>19.2 mA</em>
<em></em>
c) power input = 
==> 0.0192 x 120 = <em>2.304 Watts</em>
Answer:
Time take to fill the standing wave to the entire length of the string is 1.3 sec.
Explanation:
Given :
The length of the one end 
, frequency of the wave 
= 2.3 Hz, wavelength of the wave λ = 1 m.
Standing wave is the example of the transverse wave, standing wave doesn't transfer energy in a medium.
We know,
∴ 
λ
Where 
speed of the standing wave.
also, ∴ 
where 
time take to fill entire length of the string.
Compare above both equation,
⇒ 
sec
Therefore, the time taken to fill entire length 0f the string is 1.3 sec.
Answer:
The maximum change in flux is 
The average induced emf 
Explanation:
From the question we are told that
The speed of the technician is 
The distance from the scanner is 
The initial magnetic field is 
The final magnetic field is 
The diameter of the loop is 
The area of the loop is mathematically represented as
![A = \pi [\frac{D}{2} ]^2](https://tex.z-dn.net/?f=A%20%20%3D%20%20%5Cpi%20%5B%5Cfrac%7BD%7D%7B2%7D%20%5D%5E2)
At maximum the change in magnetic field is mathematically represented as
=> 
The average induced emf is mathematically represented as
<span>11.823 cm
There is a slight ambiguity with this question in that I don't know if the measurements are from the surface of the ball, or the center of the ball. I will take this question literally and as such the point light source will be 124 cm from the wall.
The key thing to remember is that ball won't be showing an effective diameter of 4 cm to the light source. Instead the shadow line is a tangent to the ball's surface. There is a right triangle where the hypotenuse is the distance from the center of the ball to the light source (42 cm), one leg of the triangle is the radius (2cm). That right triangle will define a chord that will be the effective diameter of the disk casting the shadow. The cosine of the half angle of the chord will be 2/42 = 1/21. The sine of the half angle then becomes sqrt(1-(1/21)^2) = sqrt(440/441) = 2sqrt(110) = 0.99886557. Now multiply that sine by 4 (radius of ball multiplied by 2 since it's the half angle and we want the full side of the chord) and we get an effective diameter of 3.995462279 cm.
Now we need to calculate the effective distance that circle is from the wall. It will be slightly larger than 82 cm. The exact value will be 82 + cos(half angle) * radius. So
82 + 1/21 * 2 = 82 + 2/21 = 82.0952381
Now we have the following dimensions with a circle replacing the ball in the original problem.
Distance from wall to effective circle = 82.0952381 cm
Distance from effective circle to point source = 124 - 82.0952381 = 41.9047619 cm
Effective diameter of circle = 3.995462279 cm
And because the geometry makes similar triangles, the following ratio applies.
3.995462279/41.9047619 = X/124
Now solve for X
3.995462279/41.9047619 = X/124
124*3.995462279/41.9047619 = X
495.4373226/41.9047619 = X
11.82293611 = X
The shadow cast on the wall will be a circle with a diameter of 11.823 cm</span>
