a 30-cm-tall, 6.0-cm-diameter cylindrical beaker is filled to its brim with water. part a what is the downward force of the wate
1 answer:
The force on the bottom of the beaker is 8.31 N.
<h3 /><h3>How can we calculate the force?</h3>To calculate the force on the bottom of the beaker we are using the formula,
F = PA
Here we are given,
A = area of the beaker.
To calculate the force we have to calculate the pressure P first.
To calculate the pressure P we are using the formula,
P= ρgh
ρ= density of water.
g= the acceleration due to gravity.
h=the height of the water.
Now we put the values in the formula, we get,
P= ρgh
Or, P= (1000)×(9.8)×(0.30)
Or, P= 2940 Pa.
From the above calculation we can say that the pressure P= 2940 Pa.
Now we put the values in the force formula,
F=PA
Or, F= 2940×
Or, F = 2940×π×(0.03)²
Or, F= 8.31N
From the above calculation we can conclude that, The force on the bottom of the beaker is 8.31 N.
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The vertical position at time t is given by
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is the initial vertical velocity of the cargo
g = 9.8 m/s^2 is the acceleration of gravity
The cargo reaches the ground when
So substituting it into the equation and solving for t, we find the time of flight of the cargo:
b) 7.5 km
The range travelled by the cargo can be calculated by considering its horizontal motion only. In fact, the horizontal motion is a uniform motion, with constant velocity equal to the initial velocity of the jet:
So the horizontal distance travelled is
And if we substitute the time of flight,
t = 22.6 s
We find the range of the cargo:
the sum of vectors with the Pythagorean theorem allows us to find that the maximum magnitude occurs for the case:
d) the two vectors are parallel
Vectors are physical quantities that have modulus and direction, for example: force, velocity, acceleration, etc.
Vector algebra has defined the sum, the product by a scalar and by a vector. The modulus and the direction of the resulting vector must be encoded.
The sum of two quantities is done using the Pythagorean theorem
c² = a² + b²
where c is the resultant called hypotenuse, a and b are the summing vectors called legs; trigonometry is used for the direction.
Let's apply this expression to the present case
a, b) perpendicular vectors
c² = a² + b²
c =
c = 11.7
the magnitude is the same in both cases, changing the direction of the vector
c) Antiparallel vectors
For this case the vectors are collinear, so the sum reduces to the algebraic addition
c = a-b
c = 6 -10
c = -4
d) parallel vectors
c = a + b
c = 4 + 10
c = 14
We can see that the vectors addition gives their maximum and minimum values when the vectors are collinear.
In conclusion using the vectors addition we find that the correct answer is
d) the two vectors are parallel
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