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:
1.308 * 10^(-5) m
Explanation:
We apply the condition for a single slit experiment:
y = (λ * D) / a
Where y = half width of fringe
λ = wavelength of light
D = distance of slit from screen
a = width of slit
We need to find a, so we make a the subject of formula:
a = (λ * D) / y
From the question:
λ = 550 nm = 550 * 10^(-9) m
D = 0.63 m
y = 0.053 / 2 = 0.0265 m
Therefore:
a = (550 * 10^(-9) * 0.63) / 0.0265
a = 1.308 * 10^(-5) m
The width of the slit is 1.308 * 10^(-5) m
Answer:
<h2>
2113 seconds</h2>
Explanation:
The general decay equation is given as 
, then;
where;
is the fraction of the radioactive substance present = 1/16
is the decay constant
t is the time taken for decay to occur = 8,450s
Before we can find the half life of the material, we need to get the decay constant first.
Substituting the given values into the formula above, we will have;
Half life f the material is expressed as 
Hence, the half life of the material is approximately 2113 seconds
The answers are to small to see.
Answer is 6.84 approx
reason:-
(2.78^2+6.25^2)^1/2=6.84 approx
