A transmission system at a radio station uses a/an _______ to convert a direct current into a highfrequency alternating current.
1 answer:
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Answer:
The rule for kilometers is that every three seconds between a lightning flash and the following thunder gives the distance to the flash in kilometers.
Explanation:
In order to use the rule of thumb to find the speed of sound in meters per second, we need to use some conversion ratios. We know there is 1 mile per every 5 seconds after the lightning is seen. We also know that there are 5280ft in 1 mile and we also know that there are 0.3048m in 1ft. This is enough information to solve this problem. We set our conversion ratios like this:
notice how the ratios were written in such a way that the units got cancelled when calculating them. Notice that in one ratio the miles were on the numerator of the fraction while on the other they were on the denominator, which allows us to cancel them. The same happened with the feet.
The problem asks us to express the answer to one significant figure so the speed of sound rounds to 300m/s.
For the second part of the problem we need to use conversions again. This time we will write our ratios backwards and take into account that there are 1000m to 1 km, so we get:
This means that for every 3.11s there will be a distance of 1km from the place where the lightning stroke. Since this is a rule of thumb, we round to the nearest integer for the calculations to be made easily, so the rule goes like this:
The rule for kilometers is that every three seconds between a lightning flash and the following thunder gives the distance to the flash in kilometers.
Answer:
51.2 mi/h
Explanation:
Total distance, d = 100 miles
First 60 miles with speed 55 mi/h
Next 40 miles with speed 75 mi/h
Time taken for first 60 miles, t1 = 60 / 55 = 1.09 h
Time taken for 40 miles, t2 = 40 / 75 = 0.533 h
Time spent to get stuck, t3 = 20 min = 0.33 h
Total time, t = t1 + t2 + t3 = 1.09 + 0.533 + 0.33 = 1.953 h
The average speed is defined as the ratio of total distance traveled to the total time taken.
Average speed =
Thus, the average speed of the journey is 51.2 mi/h.
Answer:v=2 m/s
Explanation:
Given
Length of string L=1.2 m
mass of pendulum m=0.25 kg
maximum inclination with vertical \theta =34
vertical Rise of Pendulum from its mean position is given by
Conserving Energy at top and bottom point
Potential Energy of sphere is converted into kinetic energy of sphere
Answer:
a) The gravitational potential energy before the cart rolls down the incline is 24.6 J.
b) The magnitude of the force that causes the cart to roll down is 5.47 N.
c) The acceleration of the cart is 2.38 m/s²
d) It takes the cart 1.94 s to reach the bottom of the incline.
e) The velocity of the cart at the bottom of the inclined plane is 4.62 m/s.
f) The kinetic energy of the cart as it reaches the bottom of the incline is 24.6 J.
g) The work done by the gravitational force is 24.6 J.
Explanation:
Hi there!
a) The gravitational potential energy is calculated using the following equation:
EP = m · g · h
Where:
EP = gravitational potential energy.
m = mass of the object.
g = acceleration due to gravity.
h = height at which the object is located.
The height of the inclined plane can be calculated using trigonomoetry:
sin 14.0° = height / lenght
sin 14.0° = height / 4.50 m
4.50 m · sin 14.0° = height
height = 1.09 m
Then, the gravitational potential energy will be:
EP = m · g · h
EP = 2.30 kg · 9.81 m/s² · 1.09 m = 24.6 J
The gravitational potential energy before the cart rolls down the incline is 24.6 J.
b) Please, see the attached figure for a graphical description of the problem and the forces acting on the cart. The force that causes the cart to accelerate down the incline is the horizontal component of the weight (Fwx in the figure). The magnitude of this force can be obtained using trigonometry:
sin 14° = Fwx / Fw
The weight of the cart (Fw) is calculated as follows:
Fw = m · g
Fw = 2.30 kg · 9.81 m/s²
Fw = 22.6 N
Then, the x-component of the weight will be:
FW · sin 14° = Fwx
22.6 N · sin 14° = Fwx
Fwx = 5.47 N
The magnitude of the force that causes the cart to roll down is 5.47 N.
c)Using the equation of Fwx we can calculate the acceleration of the cart:
Fwx = m · a
Where "m" is the mass of the cart and "a" is the acceleration.
Fwx / m = a
5.47 N / 2.30 kg = a
a = 2.38 m/s²
The acceleration of the cart is 2.38 m/s²
d) To calculate the time it takes the cart to reach the bottom of the incline, let´s use the equation of position of the cart:
x = x0 + v0 · t + 1/2 · a · t²
Where:
x = position of the cart at time t.
x0 = initial position.
v0 = initial velocity.
a = acceleration.
t = time.
Considering the initial position as the point at which the cart starts rolling (x0 = 0) and knowing that the cart starts from rest (v0 = 0), let´s find the time it takes the cart to travel the 4.50 m of the inclined plane:
x = 1/2 · a · t²
4.50 m = 1/2 · 2.38 m/s² · t²
2 · 4.50 m / 2.38 m/s² = t²
t = 1.94 s
It takes the cart 1.94 s to reach the bottom of the incline.
e) The velocity of the cart at the bottom of the inclined plane can be obtained using the following equation:
v = v0 + a · t
v = 0 m/s + 2.38 m/s² · 1.94 s
v = 4.62 m/s
The velocity of the cart at the bottom of the inclined plane is 4.62 m/s.
f) The kinetic energy can be calculated using the following equation:
KE = 1/2 · m · v²
Where:
KE = kinetic energy.
m = mass of the cart.
v = velocity of the cart.
KE = 1/2 · 2.30 kg · (4.62 m/s)²
KE = 24.6 J
The kinetic energy of the cart as it reaches the bottom of the incline is 24.6 J.
The gain of kinetic energy is equal to the loss of gravitational potential energy.
g) The work done by the gravitational force can be calculated using the work-energy theorem: the work done by the gravitational force is equal to the negative change in the gravitational potential energy:
W = -ΔPE
W = -(final potential energy - initial potential energy)
W = -(0 - 24.6 J)
W = 24.6 J
This can also be calculated using the definition of work:
W = Fw · d
Where "d" is the distance traveled in the direction of the force, that is the height of the inclined plane:
W = 22.6 N · 1.09 m = 24.6 J.
The work done by the gravitational force is 24.6 J.
