Explanation:
thermal expansion ∝L = (δL/δT)÷L ----(1)
δL = L∝L + δT ----(2)
we have δL = 12.5x10⁻⁶
length l = 200mm
δT = 115°c - 15°c = 100°c
putting these values into equation 1, we have
δL = 200*12.5X10⁻⁶x100
= 0.25 MM
L₂ = L + δ L
= 200 + 0.25
L₂ = 200.25mm
12.5X10⁻⁶ *115-15 * 20
= 0.025
20 +0.025
D₂ = 20.025
as this rod undergoes free expansion at 115°c, the stress on this rod would be = 0
Answer:
a)
, b)
, c) ![a = -0.128\,\frac{ft}{s^{2}}](https://tex.z-dn.net/?f=a%20%3D%20-0.128%5C%2C%5Cfrac%7Bft%7D%7Bs%5E%7B2%7D%7D)
Explanation:
a) The deceleration experimented by the commuter train in the first 2.5 miles is:
![a=\frac{[(15\,\frac{mi}{h} )\cdot (\frac{5280\,ft}{1\,mi} )\cdot (\frac{1\,h}{3600\,s} )]^{2}-[(50\,\frac{mi}{h} )\cdot (\frac{5280\,ft}{1\,mi} )\cdot (\frac{1\,h}{3600\,s} )]^{2}}{2\cdot (2.5\,mi)\cdot (\frac{5280\,ft}{1\,mi} )}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B%5B%2815%5C%2C%5Cfrac%7Bmi%7D%7Bh%7D%20%29%5Ccdot%20%28%5Cfrac%7B5280%5C%2Cft%7D%7B1%5C%2Cmi%7D%20%29%5Ccdot%20%28%5Cfrac%7B1%5C%2Ch%7D%7B3600%5C%2Cs%7D%20%29%5D%5E%7B2%7D-%5B%2850%5C%2C%5Cfrac%7Bmi%7D%7Bh%7D%20%29%5Ccdot%20%28%5Cfrac%7B5280%5C%2Cft%7D%7B1%5C%2Cmi%7D%20%29%5Ccdot%20%28%5Cfrac%7B1%5C%2Ch%7D%7B3600%5C%2Cs%7D%20%29%5D%5E%7B2%7D%7D%7B2%5Ccdot%20%282.5%5C%2Cmi%29%5Ccdot%20%28%5Cfrac%7B5280%5C%2Cft%7D%7B1%5C%2Cmi%7D%20%29%7D)
![a = -0.185\,\frac{ft}{s^{2}}](https://tex.z-dn.net/?f=a%20%3D%20-0.185%5C%2C%5Cfrac%7Bft%7D%7Bs%5E%7B2%7D%7D)
The time required to travel is:
![t = \frac{(15\,\frac{mi}{h} )\cdot (\frac{5280\,ft}{1\,fi} )\cdot(\frac{1\,h}{3600\,s} )-(50\,\frac{mi}{h} )\cdot (\frac{5280\,ft}{1\,fi} )\cdot(\frac{1\,h}{3600\,s} )}{-0.185\,\frac{ft}{s^{2}} }](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%2815%5C%2C%5Cfrac%7Bmi%7D%7Bh%7D%20%29%5Ccdot%20%28%5Cfrac%7B5280%5C%2Cft%7D%7B1%5C%2Cfi%7D%20%29%5Ccdot%28%5Cfrac%7B1%5C%2Ch%7D%7B3600%5C%2Cs%7D%20%29-%2850%5C%2C%5Cfrac%7Bmi%7D%7Bh%7D%20%29%5Ccdot%20%28%5Cfrac%7B5280%5C%2Cft%7D%7B1%5C%2Cfi%7D%20%29%5Ccdot%28%5Cfrac%7B1%5C%2Ch%7D%7B3600%5C%2Cs%7D%20%29%7D%7B-0.185%5C%2C%5Cfrac%7Bft%7D%7Bs%5E%7B2%7D%7D%20%7D)
![t = 277.477\,s\,(4.625\min)](https://tex.z-dn.net/?f=t%20%3D%20277.477%5C%2Cs%5C%2C%284.625%5Cmin%29)
b) The commuter train must stop when it reaches the station to receive passengers. Hence, speed of train must be
.
c) The final constant deceleration is:
![a = \frac{(0\,\frac{mi}{h} )\cdot (\frac{5280\,ft}{1\,mi} )\cdot(\frac{1\,h}{3600\,s} )-(15\,\frac{mi}{h} )\cdot (\frac{5280\,ft}{1\,mi} )\cdot(\frac{1\,h}{3600\,s} )}{(2.875\,min)\cdot (\frac{60\,s}{1\,min} )}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B%280%5C%2C%5Cfrac%7Bmi%7D%7Bh%7D%20%29%5Ccdot%20%28%5Cfrac%7B5280%5C%2Cft%7D%7B1%5C%2Cmi%7D%20%29%5Ccdot%28%5Cfrac%7B1%5C%2Ch%7D%7B3600%5C%2Cs%7D%20%29-%2815%5C%2C%5Cfrac%7Bmi%7D%7Bh%7D%20%29%5Ccdot%20%28%5Cfrac%7B5280%5C%2Cft%7D%7B1%5C%2Cmi%7D%20%29%5Ccdot%28%5Cfrac%7B1%5C%2Ch%7D%7B3600%5C%2Cs%7D%20%29%7D%7B%282.875%5C%2Cmin%29%5Ccdot%20%28%5Cfrac%7B60%5C%2Cs%7D%7B1%5C%2Cmin%7D%20%29%7D)
![a = -0.128\,\frac{ft}{s^{2}}](https://tex.z-dn.net/?f=a%20%3D%20-0.128%5C%2C%5Cfrac%7Bft%7D%7Bs%5E%7B2%7D%7D)
Answer:
![F = 641,771.52 \dfrac{lb-ft}{s^2}](https://tex.z-dn.net/?f=F%20%3D%20641%2C771.52%20%5Cdfrac%7Blb-ft%7D%7Bs%5E2%7D)
Explanation:
Given that
R=8 ft
Width= 10 ft
We know that hydro statics force given as
F=ρ g A X
ρ is the density of fluid
A projected area on vertical plane
X is distance of center mass of projected plane from free surface of water.
Here
X=8/2 ⇒X=4 ft
A=8 x 10=80 ![ft^2](https://tex.z-dn.net/?f=ft%5E2)
So now putting the values
F=ρ g A X
F=62.4(32.14)(80)(4)
![F = 641,771.52 \dfrac{lb-ft}{s^2}](https://tex.z-dn.net/?f=F%20%3D%20641%2C771.52%20%5Cdfrac%7Blb-ft%7D%7Bs%5E2%7D)
Answer:
ΔT= 11.94 °C
Explanation:
Given that
mass of water = 10 kh
Time t= 15 min
Heat lot from water = 400 KJ
Heat input to the water = 1 KW
Heat input the water= 1 x 15 x 60
=900 KJ
By heat balancing
Heat supply - heat rejected = Heat gain by water
As we know that heat capacity of water
![C_p=4.187 \frac{KJ}{kg-K}](https://tex.z-dn.net/?f=C_p%3D4.187%20%5Cfrac%7BKJ%7D%7Bkg-K%7D)
![Q=mC_p\Delta T](https://tex.z-dn.net/?f=Q%3DmC_p%5CDelta%20T)
Now by putting the values
900 - 400 = 10 x 4.187 x ΔT
So rise in temperature of water ΔT= 11.94 °C