Answer:
29.5 m/s
Explanation:
Volumetric flowrate = (average velocity of flow) × (cross sectional area)
Volumetric flowrate = 0.111 liters/s = 0.000111 m³/s
Cross sectional Area of flow = πr²
Diameter = 0.00579 m,
Radius, r = d/2 = 0.002895 m
A = π(0.002895)² = 0.0000037629 m²
Velocity of flow = (volumetric flow rate)/(cross sectional Area of flow)
v = 0.000111/0.0000037629
v = 29.5 m/s
Answer:
C 350W
Explanation:
Given power output to walk on a flat ground to be 300W, h = 0.05x, v = 1.4m/s
m = 70kg and g =9.8m/s².
x = horizontal distance covered
Total energy used = potential energy used in climbing and the energy used in a walking the horizontal distance.
E = mgh + 300t
Where t is the time taken to cover the distance
x = vt and h = 0.05vt
So
E = mg×0.05×vt + 300t
Substituting respective values
E = 70×9.8×0.05×1.4t +300t = 348t
P = E/t = 348W ≈ 350W.
Answer:
s=1721.344m ,v=104.96m/s.
Explanation:
using thr equation of motion;
![s=ut+\frac{1}{2}at^{2}](https://tex.z-dn.net/?f=s%3Dut%2B%5Cfrac%7B1%7D%7B2%7Dat%5E%7B2%7D)
u=0, plane starts from rest,
![s=\frac{1}{2}at^{2}](https://tex.z-dn.net/?f=s%3D%5Cfrac%7B1%7D%7B2%7Dat%5E%7B2%7D)
![a=3.2m/s^{2}, t=32.8s \\ s=\frac{1}{2}*3.2*32.8^{2}](https://tex.z-dn.net/?f=a%3D3.2m%2Fs%5E%7B2%7D%2C%20t%3D32.8s%20%5C%5C%20s%3D%5Cfrac%7B1%7D%7B2%7D%2A3.2%2A32.8%5E%7B2%7D)
s=1721.344m
v=u+at
v=0 +3.2*32.8
v=104.96m/s
Given: Wavelength λ = 410 nm convert to Meters m = 4.10 x 10⁻⁷ m
Speed of light c = 3 x 10⁸ m/s
Required: Frequency f = ?
Formula: c = λf
f = c/λ
f = 3 x 10⁸ m/s/4.10 x 10⁻⁷ m
f = 7.32 x 10¹⁴/s or 732 Thz (Terahertz)
Answer:
(a) ![W_c=127.008 J](https://tex.z-dn.net/?f=W_c%3D127.008%20J)
(b) ![W_g=148.176 J](https://tex.z-dn.net/?f=W_g%3D148.176%20J)
(c) K.E. = 21.168 J
(d) ![v=3.4293m.s^{-1}](https://tex.z-dn.net/?f=v%3D3.4293m.s%5E%7B-1%7D)
Explanation:
Given:
- mass of a block, M = 3.6 kg
- initial velocity of the block,
![u=0 m.s^{-1}](https://tex.z-dn.net/?f=u%3D0%20m.s%5E%7B-1%7D)
- constant downward acceleration,
![a_d= \frac{g}{7}](https://tex.z-dn.net/?f=a_d%3D%20%5Cfrac%7Bg%7D%7B7%7D)
That a constant upward acceleration of
is applied in the presence of gravity.
∴![a=- \frac{6g}{7}](https://tex.z-dn.net/?f=a%3D-%20%5Cfrac%7B6g%7D%7B7%7D)
- height through which the block falls, d = 4.2 m
(a)
Force by the cord on the block,
![F_c= M\times a](https://tex.z-dn.net/?f=F_c%3D%20M%5Ctimes%20a)
![F_c=3.6\times (-6)\times\frac{9.8}{7}](https://tex.z-dn.net/?f=F_c%3D3.6%5Ctimes%20%28-6%29%5Ctimes%5Cfrac%7B9.8%7D%7B7%7D)
![F_c=-30.24 N](https://tex.z-dn.net/?f=F_c%3D-30.24%20N)
∴Work by the cord on the block,
![W_c= F_c\times d](https://tex.z-dn.net/?f=W_c%3D%20F_c%5Ctimes%20d)
![W_c= -30.24\times 4.2](https://tex.z-dn.net/?f=W_c%3D%20-30.24%5Ctimes%204.2)
We take -ve sign because the direction of force and the displacement are opposite to each other.
![W_c=-127.008 J](https://tex.z-dn.net/?f=W_c%3D-127.008%20J)
(b)
Force on the block due to gravity:
![F_g= M.g](https://tex.z-dn.net/?f=F_g%3D%20M.g)
∵the gravity is naturally a constant and we cannot change it
![F_g=3.6\times 9.8](https://tex.z-dn.net/?f=F_g%3D3.6%5Ctimes%209.8)
![F_g=35.28 N](https://tex.z-dn.net/?f=F_g%3D35.28%20N)
∴Work by the gravity on the block,
![W_g=F_g\times d](https://tex.z-dn.net/?f=W_g%3DF_g%5Ctimes%20d)
![W_g=35.28\times 4.2](https://tex.z-dn.net/?f=W_g%3D35.28%5Ctimes%204.2)
![W_g=148.176 J](https://tex.z-dn.net/?f=W_g%3D148.176%20J)
(c)
Kinetic energy of the block will be equal to the net work done i.e. sum of the two works.
mathematically:
![K.E.= W_g+W_c](https://tex.z-dn.net/?f=K.E.%3D%20W_g%2BW_c)
![K.E.=148.176-127.008](https://tex.z-dn.net/?f=K.E.%3D148.176-127.008)
K.E. = 21.168 J
(d)
From the equation of motion:
![v^2=u^2+2a_d\times d](https://tex.z-dn.net/?f=v%5E2%3Du%5E2%2B2a_d%5Ctimes%20d)
putting the respective values:
![v=\sqrt{0^2+2\times \frac{9.8}{7}\times 4.2 }](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B0%5E2%2B2%5Ctimes%20%5Cfrac%7B9.8%7D%7B7%7D%5Ctimes%204.2%20%7D)
is the speed when the block has fallen 4.2 meters.