Rollercoasters generate speed by converting gravitational potential energy into kinetic energy by taking the cart to the top of a large hill and letting it go. The conversion of a perfectly efficient system would be like so:
PE = KE
and using the formulas for potential and kinetic energy:
mgh = 1/2mv^2.
However, the efficiency of this system is 50%, meaning that the kinetic energy obtained from this conversion would appear as so:
PE=0.5 KE
mgh=0.5(1/2mv^2)
mgh=1/4mv^2.
The masses cancel out, leaving:
gh=1/4v^2
The goal is to achieve 65 m/s, and with Earth’s innate gravity of 9.806 m/s^2, we have:
gh=1/4v^2
(9.806)h=1/4(65)^2
h=107.71 meters
The height of the first hill must be 107.7 meters to generate a speed of 65 m/s with a conversion efficiency of 50%.
Hope this helps!
Answer:
Concept: Physics analysis
- We have a distance vs time graph
- That indicates that we are analyzing the distance traveled by either a person or a particle
- The runner starts at 4 meters and over the interval of a second runs to 12 meters reaching the 16 meter mark. The runner stood at 16 meter mark for one full second and then runs back 10 meter over the course of one second reaching 6 meter. The runner runs forward again for a second traveling 6 meters, ending at the 12 meter mark.
Answer:
<em><u>The potential area of wind power in the country is about 6074 sq. km with wind power density greater than 300 watt/m2. More than 3,000 MW of electricity could be generated at 5 MW per sq km. The commercially viable wind potential of the country is estimated to be only about 448 MW.</u></em>
Well, I'll try to write the formula in a way that's not confusing,
but I'm afraid it might be slightly confusing anyway.
When you're working with dB, the basic rule is
A change of 10 dB means either multiplying or dividing by 10 .
Multiply something by 10 ==> it increases by 10 dB.
Divide something by 10 ==> it decreases by 10 dB.
It turns out that another way to write all of this is . . .
An increase of 10 dB ===> multiply the original amount by 10¹
An increase of 20 dB ===> multiply the original amount by 10²
An increase of, say, 7 dB ===> multiply the original amount by 10⁰·⁷
A decrease of 10 dB ===> multiply the original amount by 10⁻¹
A decrease of 30 dB ===> multiply the original amount by 10⁻³
A decrease of, say, 13 dB ===> multiply the original amount by 10⁻¹·³
This question says: The sound increases by 5 dB .
That means the original 'intensity' or 'power' of the sound
is multiplied by
10⁰·⁵ = √10 = about 3.162 (rounded) .
From the choices listed, the closest one is (c).
The period will be the same if the amplitude of the motion is increased to 2a
What is an Amplitude?
Amplitude refers to the maximum extent of a vibration or oscillation, measured from the position of equilibrium.
Here,
mass m is attached to the spring.
mass attached = m
time period = t
We know that,
The time period for the spring is calculated with the equation:
Where k is the spring constant
Now if the amplitude is doubled, it means that the distance from the equilibrium position to the displacement is doubled.
From the equation, we can say,
Time period of the spring is independent of the amplitude.
Hence,
Increasing the amplitude does not affect the period of the mass and spring system.
Learn more about time period here:
<u>brainly.com/question/13834772</u>
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