Answer:
Explanation:
The acceleration of gravity is 9.8m/s^2.
So to calculate the time it will take to make the ball stop(which btw means the ball now reach its greatest height), use the formula V1=V0+at. V1 is the final velocity(which is 0), V0 is the starting velocity(which is 30m/s), and the a(cceleration) is 9.8m/s^2.
(You can ignore the fact "at" is -30 instead 30, it's because the directions two velocity travel are opposite. )
We can now know the time it takes to make the ball stop just by the gravitational force is about 3 sec.
Use another formula S=1/2at^2, to find out the S(height) is 1/2*9.8*3^2=44.1, which is approximately D.45m .
Answer:
a).
kJ/kg
b).
kJ/kg-K
Explanation:
a). The energy rate balance equation in the control volume is given by
![\dot{Q} - \dot{W}+m(h_{1}-h_{2})=0](https://tex.z-dn.net/?f=%5Cdot%7BQ%7D%20-%20%5Cdot%7BW%7D%2Bm%28h_%7B1%7D-h_%7B2%7D%29%3D0)
![\frac{\dot{Q}}{m} = \frac{\dot{W}}{m}+m(h_{1}-h_{2})](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cdot%7BQ%7D%7D%7Bm%7D%20%3D%20%5Cfrac%7B%5Cdot%7BW%7D%7D%7Bm%7D%2Bm%28h_%7B1%7D-h_%7B2%7D%29)
![\frac{\dot{W}}{m}= \frac{\dot{Q}}{m}+c_{p}(T_{1}-T_{2})](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cdot%7BW%7D%7D%7Bm%7D%3D%20%5Cfrac%7B%5Cdot%7BQ%7D%7D%7Bm%7D%2Bc_%7Bp%7D%28T_%7B1%7D-T_%7B2%7D%29)
![\frac{\dot{W}}{m}= -30+1.1(980-670)](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cdot%7BW%7D%7D%7Bm%7D%3D%20-30%2B1.1%28980-670%29)
kJ/kg
b). Entropy produced from the entropy balance equation in a control volume is given by
![\frac{\dot{Q}}{T_{boundary}}+\dot{m}(s_{1}-s_{2})+\dot{\sigma _{gen}}=0](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cdot%7BQ%7D%7D%7BT_%7Bboundary%7D%7D%2B%5Cdot%7Bm%7D%28s_%7B1%7D-s_%7B2%7D%29%2B%5Cdot%7B%5Csigma%20_%7Bgen%7D%7D%3D0)
![\frac{\dot{\sigma _{gen}}}{m}=\frac{-\frac{\dot{Q}}{m}}{T_{boundary}}+(s_{2}-s_{1})](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cdot%7B%5Csigma%20_%7Bgen%7D%7D%7D%7Bm%7D%3D%5Cfrac%7B-%5Cfrac%7B%5Cdot%7BQ%7D%7D%7Bm%7D%7D%7BT_%7Bboundary%7D%7D%2B%28s_%7B2%7D-s_%7B1%7D%29)
![\frac{\dot{\sigma _{gen}}}{m}=\frac{-\frac{\dot{Q}}{m}}{T_{boundary}}+c_{p}ln\frac{T_{2}}{T_{1}}-R.ln\frac{p_{2}}{p_{1}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cdot%7B%5Csigma%20_%7Bgen%7D%7D%7D%7Bm%7D%3D%5Cfrac%7B-%5Cfrac%7B%5Cdot%7BQ%7D%7D%7Bm%7D%7D%7BT_%7Bboundary%7D%7D%2Bc_%7Bp%7Dln%5Cfrac%7BT_%7B2%7D%7D%7BT_%7B1%7D%7D-R.ln%5Cfrac%7Bp_%7B2%7D%7D%7Bp_%7B1%7D%7D)
![\frac{\dot{\sigma _{gen}}}{m}=\frac{-30}{315}+1.1ln\frac{670}{980}-0.287.ln\frac{100}{400}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cdot%7B%5Csigma%20_%7Bgen%7D%7D%7D%7Bm%7D%3D%5Cfrac%7B-30%7D%7B315%7D%2B1.1ln%5Cfrac%7B670%7D%7B980%7D-0.287.ln%5Cfrac%7B100%7D%7B400%7D)
![\frac{\dot{\sigma _{gen}}}{m}=0.0952+0.4183+0.3978](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cdot%7B%5Csigma%20_%7Bgen%7D%7D%7D%7Bm%7D%3D0.0952%2B0.4183%2B0.3978)
kJ/kg-K
Answer:
Angular speed ω=3771.4 rad/min
Revolution=5921 rpm
Explanation:
Given data
![d=28in\\r=d/2=28/2=14in\\v=50mi/hr](https://tex.z-dn.net/?f=d%3D28in%5C%5Cr%3Dd%2F2%3D28%2F2%3D14in%5C%5Cv%3D50mi%2Fhr)
To find
Angular speed ω
Revolution per minute N
Solution
First we need to convert the speed of truck to inches per mile
as
1 mile=63360 inches
1 hour=60 minutes
so
![v=(50*\frac{63360}{60} )\\v=52800in/min](https://tex.z-dn.net/?f=v%3D%2850%2A%5Cfrac%7B63360%7D%7B60%7D%20%29%5C%5Cv%3D52800in%2Fmin)
Now to solve for angular speed ω by substituting the speed v and radius r in below equation
![w=\frac{v}{r}\\ w=\frac{52800in/min}{14in}\\ w=3771.4rad/min](https://tex.z-dn.net/?f=w%3D%5Cfrac%7Bv%7D%7Br%7D%5C%5C%20w%3D%5Cfrac%7B52800in%2Fmin%7D%7B14in%7D%5C%5C%20w%3D3771.4rad%2Fmin)
To solve for N(revolutions per minute) by substituting the angular speed ω in the following equation
The way I do it is suddenly, in the same sort of way that magicians try to pull a table cloth off a table when there's things on the table cloth.The sudden approach acts as an impulse of force and starts to accelerate the roll. But, the piece (assuming it has perforations) is off the roll before the roll can move, due to inertia. Then the roll will acclerate, move, slow down and stop. However, in accelerating, the roll will unravel. The bigger the impulse the more it will unravel.+++++++++++++++++++++++++++++++++++++++If on the other hand, the piece of paper is held firmly, and the roll is pulled, then the impulse is presumably given to the paper and the hand whose inertia is a lot more than that of the roll. So, I think I'd actually go for choice c)+++++++++++++++++++++++++++++++++++++This assumes that the roll is free to rotate.I think that a similar idea is behind the design and use of a "ballistic galvanometer". The charge is passed through the galvanometer quickly, as a current pulse. Then the needle starts to deflect, and the deflection is arranged to depend on the total charge that has passed through in the time of the current pulse.
For astronomical objects, the time period can be calculated using:
T² = (4π²a³)/GM
where T is time in Earth years, a is distance in Astronomical units, M is solar mass (1 for the sun)
Thus,
T² = a³
a = ∛(29.46²)
a = 0.67 AU
1 AU = 1.496 × 10⁸ Km
0.67 * 1.496 × 10⁸ Km
= 1.43 × 10⁹ Km