Answer:
Explanation:
Let the tension in the string be T . At the top of the circle , total force acting on them = T + mg . This will provide centripetal force
T + mg = m v² / r
4 + .25 x 9.8 = .25 x v² / .62
6.45 = .25 v² / .62
v² = 16
v = 4 m /s .
The internal energy of the gas is 49,200 J
Explanation:
The internal energy of a diatomic gas, such as
, is given by

where
n is the number of moles
R is the gas constant
T is the absolute temperature of the gas
For the gas in this problem, we have:
n = 4.50 (number of moles)
R = 8.31 J/(mol·K) (gas constant)
(absolute temperature)
Substituting, we find:

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Answer:
The speed decreases.
Explanation:
This can be explained using the conservation of linear momentum.
Since there is no friction, the initial moment of the train must be equal to its linear moment after it is filled with water.
the initial linear momentum is

where
is the initial mass of the train, and
the initial speed of the train.
And linear momentum after the water filled the train car is

where
is mass of the train after the rain, and
the speed of the train after the rain
<u>the equality must be fulfilled:</u>

We know that if water is added to the train,
that is the mass after the water is added, is greater than
which is the mass of the train without the water.
Therefore, in order for the conservation of the linear momentum to be fulfilled: 
the speed after the water is added (
) must be smaller than the initial train speed (
) . So the speed of the car decreases.
Answer:
0.546 
Explanation:
From the given information:
The force on a given current-carrying conductor is:

where the length usually in negative (x) direction can be computed as

Now, taking the integral of the force between x = 1.0 m and x = 3.0 m to get the value of the force, we have:



![F = I (9.0) \bigg [\dfrac{x^3}{3} \bigg ] ^3_1 \hat k](https://tex.z-dn.net/?f=F%20%3D%20I%20%20%289.0%29%20%5Cbigg%20%5B%5Cdfrac%7Bx%5E3%7D%7B3%7D%20%5Cbigg%20%5D%20%5E3_1%20%5Chat%20k)
![F = I (9.0) \bigg [\dfrac{3^3}{3} - \dfrac{1^3}{3} \bigg ] \hat k](https://tex.z-dn.net/?f=F%20%3D%20I%20%20%289.0%29%20%5Cbigg%20%5B%5Cdfrac%7B3%5E3%7D%7B3%7D%20-%20%5Cdfrac%7B1%5E3%7D%7B3%7D%20%5Cbigg%20%5D%20%20%5Chat%20k)
where;
current I = 7.0 A
![F = (7.0 \ A) (9.0) \bigg [\dfrac{27}{3} - \dfrac{1}{3} \bigg ] \hat k](https://tex.z-dn.net/?f=F%20%3D%20%287.0%20%5C%20A%29%20%20%289.0%29%20%5Cbigg%20%5B%5Cdfrac%7B27%7D%7B3%7D%20-%20%5Cdfrac%7B1%7D%7B3%7D%20%5Cbigg%20%5D%20%20%5Chat%20k)
![F = (7.0 \ A) (9.0) \bigg [\dfrac{26}{3} \bigg ] \hat k](https://tex.z-dn.net/?f=F%20%3D%20%287.0%20%5C%20A%29%20%20%289.0%29%20%5Cbigg%20%5B%5Cdfrac%7B26%7D%7B3%7D%20%5Cbigg%20%5D%20%20%5Chat%20k)
F = 546 × 10⁻³ T/mT 
F = 0.546 