Answer:
a. 192 m/s
b. -17,760 kPa
Explanation:
First let's write the flow rate of the liquid, using the following equation:
Q = A*v
Where Q is the flow rate, A is the cross section area of the pipe (A = pi * radius^2) and v is the speed of the liquid. The flow rate in both parts of the pipe (larger radius and smaller radius) needs to be the same, so we have:
a.
A1*v1 = A2*v2
pi * 0.02^2 * 12 = pi * 0.005^2 * v2
v2 = 0.02^2 * 12 / 0.005^2
v2 = 192 m/s
b.
To find the pressure of the other side, we need to use the Bernoulli equation: (600 kPa = 600000 N/m2)
P1 + d1*v1^2/2 = P2 + d1*v2^2/2
Where d1 is the density of the liquid (for water, we have d1 = 1000 kg/m3)
600000 + 1000*12^2/2 = P2 + 1000*192^2/2
P2 = 600000 + 72000 - 1000*192^2/2
P2 = -17760000 N/m2 = -17,760 kPa
The speed in the smaller part of the pipe is too high, the negative pressure in the second part means that the inicial pressure is not enough to maintain this output speed.
Answer:
a) 5 m/s
b) 17.8542 m/s
c) 24.7212 m/s
0.229
Explanation:
t = Time taken
u = Initial velocity = 5 m/s
v = Final velocity
s = Displacement
a = Acceleration due to gravity = 9.81 m/s²


So, the stone would travel 1.27 m up

Velocity as the rock passes through the original point is 5 m/s

Time taken to reach the original point is 0.51+0.51 = 1.02 seconds
So, total height of the rock would fall is 30+1.27 = 31.27 m

Time taken by the stone to reach 15 m above the ground is 1.82+0.51 = 2.33 seconds

Speed of the ball at 15 m above the ground is 17.8542 m/s


Speed of the stone just before it hits the street is 24.7212 m/s
F = Force
m = Mass = 100 kg
g = Acceleration due to gravity = 9.81 m/s²
s = Displacement = 4 km = 4000 m
P = Power = 1 hp = 745.7 Watt
t = Time taken = 20 minutes = 1200 seconds
μ = Coefficient of sliding friction
F = μ×m×g
⇒F = μ×100×9.81
W = Work done = F×s
P = Work done / Time
⇒P = F×s / t

Coefficient of sliding friction is 0.229