Answer:
v = 31.84 cm/s or 0.318 m/s
the speed of the water leaving the end of the hose is 31.84 cm/s or 0.318 m/s
Explanation:
Given;
Diameter of hose d = 2.76 cm
Volume filled V = 20.0 L = 20,000 cm^3
Time t = 1.45 min = 105 seconds
The volumetric flow rate of water is;
F = V/t = 20,000cm^3 ÷ 105 seconds
F = 190.48 cm^3/s
The volumetric flow rate is equal the cross sectional area of pipe multiply by the speed of flow.
F = Av
v = F/A
Area A = πd^2/4
Speed v = F/(πd^2/4)
v = 4F/πd^2 ......1
Substituting the given values;
v = (4×190.48)/(π×2.76^2)
v = 31.83767439628 cm/s
v = 31.84 cm/s or 0.318 m/s
the speed of the water leaving the end of the hose is 31.84 cm/s or 0.318 m/s
Answer:
i) E = 269 [MJ] ii)v = 116 [m/s]
Explanation:
This is a problem that encompasses the work and principle of energy conservation.
In this way, we establish the equation for the principle of conservation and energy.
i)

![W_{1-2}= (F*d) - (m*g*h)\\W_{1-2}=(500000*2.5*10^3)-(40000*9.81*2.5*10^3)\\W_{1-2}= 269*10^6[J] or 269 [MJ]](https://tex.z-dn.net/?f=W_%7B1-2%7D%3D%20%28F%2Ad%29%20-%20%28m%2Ag%2Ah%29%5C%5CW_%7B1-2%7D%3D%28500000%2A2.5%2A10%5E3%29-%2840000%2A9.81%2A2.5%2A10%5E3%29%5C%5CW_%7B1-2%7D%3D%20269%2A10%5E6%5BJ%5D%20or%20269%20%5BMJ%5D)
At that point the speed 1 is equal to zero, since the maximum height achieved was 2.5 [km]. So this calculated work corresponds to the energy of the rocket.
Er = 269*10^6[J]
ii ) With the energy calculated at the previous point, we can calculate the speed developed.
![E_{k2}=0.5*m*v^2\\269*10^6=0.5*40000*v^2\\v=\sqrt{\frac{269*10^6}{0.5*40000} }\\ v=116[m/s]](https://tex.z-dn.net/?f=E_%7Bk2%7D%3D0.5%2Am%2Av%5E2%5C%5C269%2A10%5E6%3D0.5%2A40000%2Av%5E2%5C%5Cv%3D%5Csqrt%7B%5Cfrac%7B269%2A10%5E6%7D%7B0.5%2A40000%7D%20%7D%5C%5C%20v%3D116%5Bm%2Fs%5D)
Answer:
g=9.64m/s^2.
Explanation:
Gravitational field strength (in other words, gravitational acceleration) is given as follows:g=GMR2g=R2GMwhere G=6.674×10−11m3kg⋅s2G=6.674×10−11kg⋅s2m3 is the gravitational constant, M=5.972×1024kgM=5.972×1024kg is the mass of the Earth, and R=6.371×106m+0.06×106m=6.431×106mR=6.371×106m+0.06×106m=6.431×106m is the distance from the center of the Earth to the required point above the surface (radius plus 60 km).
Answer:
0.02896 kg/s
Explanation:
= Initial displacement = 0.5 m
= Final displacement = 0.1 m
t = Time taken = 0.5 s
m = Mass of object = 45 g
Displacement is given by

At maximum displacement


The magnitude of the damping coefficient is 0.02896 kg/s
Answer with Explanation:
Mass of pendulum bob, m=0.453 kg
Speed,
2.58 m/s
a.r=75.1 cm=
=0.751 m

Tension in the pendulum cable is given by
Tension=Centripetal force+force due to gravity

Where 
Substitute the values


b.When the pendulum reaches its highest point,then
Final velocity, 
According to law of conservation of energy



Substitute the values



The angle mad by cable with the vertical=

c.When the pendulum reaches at highest point then
Acceleration, a=0
Therefore, the tension in the pendulum cable

Substitute the values

