The force required to pull the two hemispheres is 46622.72N
<h3>Calculation and Parameters</h3>
( Note: 1 millibar=100 N/m2. One atmosphere is 1013 millibar = 1.013×105 N/m2 ]
The contact area between the hemispheres is (pi x 0.400^2) = 0.5024m^2.
Pressure difference = (940 - 12)
= 928 millibars.
(928 x 100)
= 92,800N/m^2.
Therefore, the required force to pull the two hemispheres is
(92800 x 0.5024)
= 46622.72N.
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Answer:
40mph
Explanation:
20miles .5 miles away if you go 20 mph you get there in a hour soo if you double to 40 mpg you get there in 0.5
Given that:
Distance , s = 18.5 m
Velocity , v = 3.85 m/s
Time , t =?
Since,
Velocity = distance/time
or
Time= distance/velocity
time= 18.5/ 3.85
time= 4.8 s
So the time elapse between the release of the ball and the ball passing home plate is 4.8 seconds.
Answer:
Length = 2.32 m
Explanation:
Let the length required be 'L'.
Given:
Resistance of the resistor (R) = 3.7 Ω
Radius of the rod (r) = 1.9 mm = 0.0019 m [1 mm = 0.001 m]
Resistivity of the material of rod (ρ) = ![1.8\times 10^{-5}\ \Omega\cdot m](https://tex.z-dn.net/?f=1.8%5Ctimes%2010%5E%7B-5%7D%5C%20%5COmega%5Ccdot%20m)
First, let us find the area of the circular rod.
Area is given as:
![A=\pi r^2=3.14\times (0.0019)^2=1.13\times 10^{-5}\ m^2](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E2%3D3.14%5Ctimes%20%280.0019%29%5E2%3D1.13%5Ctimes%2010%5E%7B-5%7D%5C%20m%5E2)
Now, the resistance of the material is given by the formula:
![R=\rho( \frac{L}{A})](https://tex.z-dn.net/?f=R%3D%5Crho%28%20%5Cfrac%7BL%7D%7BA%7D%29)
Express this in terms of 'L'. This gives,
![\rho\times L=R\times A\\\\L=\frac{R\times A}{\rho}](https://tex.z-dn.net/?f=%5Crho%5Ctimes%20L%3DR%5Ctimes%20A%5C%5C%5C%5CL%3D%5Cfrac%7BR%5Ctimes%20A%7D%7B%5Crho%7D)
Now, plug in the given values and solve for length 'L'. This gives,
![L=\frac{3.7\ \Omega\times 1.13\times 10^{-5}\ m^2}{1.8\times 10^{-5}\ \Omega\cdot m}\\\\L=\frac{4.181}{1.8}=2.32\ m](https://tex.z-dn.net/?f=L%3D%5Cfrac%7B3.7%5C%20%5COmega%5Ctimes%201.13%5Ctimes%2010%5E%7B-5%7D%5C%20m%5E2%7D%7B1.8%5Ctimes%2010%5E%7B-5%7D%5C%20%5COmega%5Ccdot%20m%7D%5C%5C%5C%5CL%3D%5Cfrac%7B4.181%7D%7B1.8%7D%3D2.32%5C%20m)
Therefore, the length of the material required to make a resistor of 3.7 Ω is 2.32 m.
1. ![I_2 = 0.14 I_1](https://tex.z-dn.net/?f=I_2%20%3D%200.14%20I_1)
Explanation:
We have:
voltage in the primary coil
voltage in the secondary coil
The efficiency of the transformer is 100%: this means that the power in the primary coil and in the secondary coil are equal
![P_1 = P_2\\V_1 I_1 = V_2 I_2](https://tex.z-dn.net/?f=P_1%20%3D%20P_2%5C%5CV_1%20I_1%20%3D%20V_2%20I_2)
where I1 and I2 are the currents in the two coils. Re-arranging the equation, we find
![\frac{I_2}{I_1}=\frac{V_1}{V_2}=\frac{15.7 V}{110 V}=0.14](https://tex.z-dn.net/?f=%5Cfrac%7BI_2%7D%7BI_1%7D%3D%5Cfrac%7BV_1%7D%7BV_2%7D%3D%5Cfrac%7B15.7%20V%7D%7B110%20V%7D%3D0.14)
which means that the current in the secondary coil is 14% of the value of the current in the primary coil.
2. 5.7 V
We can solve the problem by using the transformer equation:
![\frac{N_p}{N_s}=\frac{V_p}{V_s}](https://tex.z-dn.net/?f=%5Cfrac%7BN_p%7D%7BN_s%7D%3D%5Cfrac%7BV_p%7D%7BV_s%7D)
where:
Np = 400 is the number of turns in the primary coil
Ns = 19 is the number of turns in the secondary coil
Vp = 120 V is the voltage in the primary coil
Vs = ? is the voltage in the secondary coil
Re-arranging the formula and substituting the numbers, we find:
![V_s = V_p \frac{N_s}{N_p}=(120 V)\frac{19}{400}=5.7 V](https://tex.z-dn.net/?f=V_s%20%3D%20V_p%20%5Cfrac%7BN_s%7D%7BN_p%7D%3D%28120%20V%29%5Cfrac%7B19%7D%7B400%7D%3D5.7%20V)