Answer:
The speed of the block is 8.2 m/s
Explanation:
Given;
mass of block, m = 2.1 kg
height above the top of the spring, h = 5.5 m
First, we determine the spring constant based on the principle of conservation of potential energy
¹/₂Kx² = mg(h +x)
¹/₂K(0.25)² = 2.1 x 9.8(5.5 +0.25)
0.03125K = 118.335
K = 118.335 / 0.03125
K = 3786.72 N/m
Total energy stored in the block at rest is only potential energy given as:
E = U = mgh
U = 2.1 x 9.8 x 5.5 = 113.19 J
Work done in compressing the spring to 15.0 cm:
W = ¹/₂Kx² = ¹/₂ (3786.72)(0.15)² = 42.6 J
This is equal to elastic potential energy stored in the spring,
Then, kinetic energy of the spring is given as:
K.E = E - W
K.E = 113.19 J - 42.6 J
K.E = 70.59 J
To determine the speed of the block due to this energy:
KE = ¹/₂mv²
70.59 = ¹/₂ x 2.1 x v²
70.59 = 1.05v²
v² = 70.59 / 1.05
v² = 67.229
v = √67.229
v = 8.2 m/s
Q = mcθ
Where Q = Amount of heat in J
m = Mass of substance in kg
θ = Temperature rise in °C or K
C = Specific heat capacity in J/kgK
From given data:
Q = 33 kJ = 33 000 J, m= 2.0 kg, θ = 80 K, c = ?
33000 = 2 * c * 80
33000 = 160c
160c = 33000
c = 33000/160 = 206.25
Therefore specific heat capacity is 206.25 J/kgK
D)
the slowest through gases, faster through liquids, and fastest through solids.
is that Right?
pls let me know
Answer:
![W=17085KJ](https://tex.z-dn.net/?f=W%3D17085KJ)
Explanation:
From the question we are told that:
Height ![H=16m](https://tex.z-dn.net/?f=H%3D16m)
Radius ![R=3](https://tex.z-dn.net/?f=R%3D3)
Height of water ![H_w=9m](https://tex.z-dn.net/?f=H_w%3D9m)
Gravity ![g=9.8m/s](https://tex.z-dn.net/?f=g%3D9.8m%2Fs)
Density of water ![\rho=1000kg/m^3](https://tex.z-dn.net/?f=%5Crho%3D1000kg%2Fm%5E3)
Generally the equation for Volume of water is mathematically given by
![dv=\pi*r^2dy](https://tex.z-dn.net/?f=dv%3D%5Cpi%2Ar%5E2dy)
![dv=\frac{\piR^2}{H^2}(H-y)^2dy](https://tex.z-dn.net/?f=dv%3D%5Cfrac%7B%5CpiR%5E2%7D%7BH%5E2%7D%28H-y%29%5E2dy)
Where
y is a random height taken to define dv
Generally the equation for Work done to pump water is mathematically given by
![dw=(pdv)g (H-y)](https://tex.z-dn.net/?f=dw%3D%28pdv%29g%20%28H-y%29)
Substituting dv
![dw=(p(=\frac{\piR^2}{H^2}(H-y)^2dy))g (H-y)](https://tex.z-dn.net/?f=dw%3D%28p%28%3D%5Cfrac%7B%5CpiR%5E2%7D%7BH%5E2%7D%28H-y%29%5E2dy%29%29g%20%28H-y%29)
![dw=\frac{\rho*g*R^2}{H^2}(H-y)^3dy](https://tex.z-dn.net/?f=dw%3D%5Cfrac%7B%5Crho%2Ag%2AR%5E2%7D%7BH%5E2%7D%28H-y%29%5E3dy)
Therefore
![W=\int dw](https://tex.z-dn.net/?f=W%3D%5Cint%20dw)
![W=\int(\frac{\rho*g*R^2}{H^2}(H-y)^3)dy](https://tex.z-dn.net/?f=W%3D%5Cint%28%5Cfrac%7B%5Crho%2Ag%2AR%5E2%7D%7BH%5E2%7D%28H-y%29%5E3%29dy)
![W=\rho*g*R^2}{H^2}\int((H-y)^3)dy)](https://tex.z-dn.net/?f=W%3D%5Crho%2Ag%2AR%5E2%7D%7BH%5E2%7D%5Cint%28%28H-y%29%5E3%29dy%29)
![W=\frac{1000*9.8*3.142*3^2}{9^2}[((9-y)^3)}^9_0](https://tex.z-dn.net/?f=W%3D%5Cfrac%7B1000%2A9.8%2A3.142%2A3%5E2%7D%7B9%5E2%7D%5B%28%289-y%29%5E3%29%7D%5E9_0)
![W=3420.84*0.25[2401-65536]](https://tex.z-dn.net/?f=W%3D3420.84%2A0.25%5B2401-65536%5D)
![W=17084965.5J](https://tex.z-dn.net/?f=W%3D17084965.5J)
![W=17085KJ](https://tex.z-dn.net/?f=W%3D17085KJ)
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