Explanation:
For each object, the initial potential energy is converted to rotational energy and translational energy:
PE = RE + KE
mgh = ½ Iω² + ½ mv²
For the marble (a solid sphere), I = ⅖ mr².
For the basketball (a hollow sphere), I = ⅔ mr².
For the manhole cover (a solid cylinder), I = ½ mr².
For the wedding ring (a hollow cylinder), I = mr².
If we say k is the coefficient in each case:
mgh = ½ (kmr²) ω² + ½ mv²
For rolling without slipping, ωr = v:
mgh = ½ kmv² + ½ mv²
gh = ½ kv² + ½ v²
2gh = (k + 1) v²
v² = 2gh / (k + 1)
The smaller the value of k, the higher the velocity. Therefore:
marble > manhole cover > basketball > wedding ring
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4. For this problem, we have to write and solve a proportion. We would set this proportion up as 12/15 = 8/x. This is because we're looking for the length of the shadow and we know the height of the items, so we line them up horizontally and x goes with 8, because we're looking for the shadow length. Let's cross multiply the values. 15 * 8 = 120. 12 * x = 12. You get 120 = 12x. Now, we must divide each side by 12 to isolate the "x". 120/12 is 10. x = 10. There. The cardboard box casts a shadow that is 10 ft long.
5. For this question, you do the same thing. This time, you're finding the height of the tower, so you would do 1.2/0.6 = x/7. Cross multiply the values in order to get 8.4 = 0.6x. Now, divide each side by 0.6x to isolate the "x". 8.4/0.6 is 14. x = 14. There. The tower is 14 m tall.
If you need more help on proportions and using proportions in real life situations, feel free to search on the internet to find more information about how you solve them.
Answer:
.
Explanation:
The frequency
of a wave is equal to the number of wave cycles that go through a point on its path in unit time (where "unit time" is typically equal to one second.)
The wave in this question travels at a speed of
. In other words, the wave would have traveled
in each second. Consider a point on the path of this wave. If a peak was initially at that point, in one second that peak would be
How many wave cycles can fit into that
? The wavelength of this wave
gives the length of one wave cycle. Therefore:
.
That is: there are
wave cycles in
of this wave.
On the other hand, Because that
of this wave goes through that point in each second, that
wave cycles will go through that point in the same amount of time. Hence, the frequency of this wave would be
Because one wave cycle per second is equivalent to one Hertz, the frequency of this wave can be written as:
.
The calculations above can be expressed with the formula:
,
where
represents the speed of this wave, and
represents the wavelength of this wave.
No it is unsafe. Even if they are empty they cannot
Answer:
The work and heat transfer for this process is = 270.588 kJ
Explanation:
Take properties of air from an ideal gas table. R = 0.287 kJ/kg-k
The Pressure-Volume relation is <em>PV</em> = <em>C</em>
<em>T = C </em> for isothermal process
Calculating for the work done in isothermal process
<em>W</em> = <em>P</em>₁<em>V</em>₁ ![ln[\frac{P_{1} }{P_{2} }]](https://tex.z-dn.net/?f=ln%5B%5Cfrac%7BP_%7B1%7D%20%7D%7BP_%7B2%7D%20%7D%5D)
= <em>mRT</em>₁
[∵<em>pV</em> = <em>mRT</em>]
= (5) (0.287) (272.039) ![ln[\frac{2.0}{1.0}]](https://tex.z-dn.net/?f=ln%5B%5Cfrac%7B2.0%7D%7B1.0%7D%5D)
= 270.588 kJ
Since the process is isothermal, Internal energy change is zero
Δ<em>U</em> = 
From 1st law of thermodynamics
Q = Δ<em>U </em>+ <em>W</em>
= 0 + 270.588
= 270.588 kJ