Ask question

Ask question

All categories

2 years ago

13

If a rainstorm drops 5 cm of rain over an area of 13 km2 in the period of 3 hours, what is the momentum (in kg · m/s) of the rai

n that falls in five seconds? Assume the terminal velocity of a raindrop is 10 m/s. (Enter the magnitude. The density of water is 1,000 kg/m3.)

1 answer:

stiks02 [169]2 years ago

4 0

To solve the problem it is necessary to apply the concepts related to Conservation of linear Moment.

The expression that defines the linear momentum is expressed as

P=mv

Where,

m=mass

v= velocity

According to our data we have to

v=10m/s

d=0.05m

$A=13*10^6m^2$

Volume $(V) = A*d = (15*10^6)(0.03) = 3.9*10^5m^3$

t = 3hours=10800s

$\rho = 1000kg/m^3$

From the given data we can calculate the volume of rain for 5 seconds

$V' = \frac{V}{t}*\Delta t_{total}$

Where,

$\Delta t_{total}$ It is the period of time we want to calculate total rainfall, that is

$V' = \frac{3.9*10^5}{10800}*5$

$V' = 1.805*10^2m^3$

Through water density we can now calculate the mass that fell during the 5 seconds:

$m' = V'*\rho$

$m' = 1.805*10^2*1000$

$m' = 1.805*10^5m^2$

Now applying the prevailing equation given we have to

$P=m'v$

$P = (1.805*10^5)(10)$

$P = 1.805*10^6 Kg.m/s$

Therefore the momentum of the rain that falls in five seconds is $1.805*10^6 Kg.m/s$

You might be interested in

Max and Jimmy want to jump on a trampoline. Max begins jumping in a steady pattern, making small waves in the trampoline. Jimmy

mylen [45]

Answer:

x_total = (A + B) cos (wt + Ф)

we have the sum of the two waves in a phase movement

Explanation:

In this case we can see that the first boy Max when he enters the trampoline and jumps creates a harmonic movement, with a given frequency. When the second boy Jimmy enters the trampoline and begins to jump he also creates a harmonic movement. If the frequency of the two movements is the same and they are in phase we have a resonant process, where the amplitude of the movement increases significantly.

Max

x₁ = A cos (wt + Ф)

Jimmy

x₂ = B cos (wt + Ф)

total movement

x_total = (A + B) cos (wt + Ф)

Therefore we have the sum of the two waves in a phase movement

8 0

1 year ago

Two resistors of resistances R1 and R2, with R2>R1, are connected to a voltage source with voltage V0. When the resistors are

ehidna [41]

Answer

The Value of r = 0.127

Explanation:

The mathematical representation of the two resistors connected in series is

$R_T = R_1 +R_2$

And from Ohm law

$I_s =\frac{ V}{R_T}$

$I_s = \frac{V_0}{R_1 +R_2} ---(1)$

The mathematical representation of the two resistors connected in parallel is

$R_T = \frac{1}{R_1} +\frac{1}{R_2}$

$= \frac{R_1 R_2}{R_1 +R_2}$

From the question $I_p =10I_s$

=> $I_p =10I_s = \frac{V_0 }{\frac{R_1R_2}{R_1 +R_2} } = \frac{V_0 (R_1 +R_2)}{R_1 R_2}---(2)$

Dividing equation 2 with equation 1

=> $\frac{10I_s}{I_s} =\frac{\frac{V_0 (R_1 +R_2)}{R_1 R_2}}{\frac{V_0}{R_1 +R_2}}$

$10 = \frac{(R_1+R_2)^2}{R_1 R_2}----(3)$

We are told that $r = \frac{R_1}{R_2} \ \ \ \ \ = > R_1 = rR_2$

From equation 3

$10 = \frac{(1-r)^2}{r}$

$=> \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1+r^2 + 2r = 10r$

$=> \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ r^2 -8r+1 = 0$

Using the quadratic formula

$r =\frac{-b\pm \sqrt{(b^2 - 4ac)} }{2a}$

a = 1 b = -8 c =1

$= \frac{8 \pm\sqrt{((-8)^2- (4*1*1))} }{2*1}$

$r= \frac{8+ \sqrt{60} }{2} \ or \ r = \frac{8 - \sqrt{60} }{2}$

$r = \ 7.87\ or \ r \ = \ 0.127$

Now r = 0.127 because it is the least value among the obtained values

4 0

1 year ago

A steel rod with a length of l = 1.55 m and a cross section of A = 4.45 cm2 is held fixed at the end points of the rod. What is

Blababa [14]

To solve this problem it is necessary to apply the concepts related to thermal stress. Said stress is defined as the amount of deformation caused by the change in temperature, based on the parameters of the coefficient of thermal expansion of the material, Young's module and the Area or area of the area.

$F = AY\alpha \Delta T$

Where

A = Cross-sectional Area

Y = Young's modulus

$\alpha$ = Coefficient of linear expansion for steel

$\Delta T$ = Temperature Raise

Our values are given as,

$A = 4.45cm^2$

$T = 37K$

$\alpha = 1.17*10^{-5}K^{-1}$

$Y = 200*10^9Gpa$

Replacing we have,

$F = (4.45*10^{-4})(200*10^9)(1.17*10^{-5})(37)$

$F = 38526.1N$

Therefore the size of the force developing inside the steel rod when its temperature is raised by 37K is 38526.1N

7 0

2 years ago

When the volcano Krakatoa erupted in 1883, it was heard 5000 km away. Which statement about the sound from the volcano is not co

lina2011 [118]

Answer a) is incorrect as sound does not travel in a vacuum.

7 0

2 years ago

A racecar driver on a flat racetrack steps on the gas, changing her velocity from 10 m/sec to 30 m/sec in 5 seconds. What is the

erastova [34]

Answer:

4m/s2

Explanation:

The following data were obtained from the question:

U (initial velocity) = 10m/s

V (final velocity) = 30m/s

t (time) = 5secs

a (acceleration) =?

Acceleration is the rate of change of velocity with time. It is represented mathematically as:

a = (V - U)/t

Now, with this equation i.e

a = (V - U)/t, we can calculate the acceleration of the race car as follow:

a = (V - U)/t

a = (30 - 10)/5

a = 20/5

a = 4m/s2

Therefore, the acceleration of the race car is 4m/s2

8 0

2 years ago

Read 2 more answers