Answer:
Explanation:
1 ) Since it is a isochoric process , heat energy passed into gas
= n Cv dT , n is no of moles of gas , Cv is specific heat at constant volume and dT is rise in temperature .
= 7.4 x 12.47 x ( 500 - 300 )
= 18455.6 J.
2 ) Since there is no change in volume , work done by the gas is constant.
3 ) from , gas law equation
PV = nRT
P = nRT / V
= 7.4 x 8.3 x 500 / .74
= .415 x 10⁵ Pa.
4 ) Average kinetic energy of gas molecules after attainment of final temperature
= 3/2 x R/ N x T
= 1.5 x 1.38 x 10⁻²³ x 500
= 1.035 x 10⁻²⁰ J
1/2 m v² = 1.035 x 10⁻²⁰
v² = 2 x 1.035 x 10⁻²⁰ / 1.39 x 10⁻²⁶
= 1.49 x 10⁶
v = 1.22 x 10³ m /s
5 ) In this process , pressure remains constant
gas is cooled from 500 to 300 K
heat will be withdrawn .
heat withdrawn
= n Cp dT
= 7.4 x 20.79 x 200
= 30769.2 J .
6 )
gas will have reduced volume due to cooling
reduced volume = .74 x 300 / 500
= .444 m³
change in volume
= .74 - .444
= .296 m³
work done on the gas
= P x dV
pressure x change in volume
= .415 x 10⁵ x .296
= 12284 J.
In physics, force is equal to mass multiplied to acceleration. We are given that the mass is 0.25 kg and the force is 20 N.
F = ma
20 N = 0.25 kg * a
20 kg*m/s^2 = 0.25 kg * a
a = 20/0.25
a = 80 m/s^2
So the acceleration of the ball is 80 m/s^2.
Answer:
The height of the water above the hole in the tank is 58 mm
Explanation:
In order to solve this problem we need to draw a sketch of the dimensions that include the input variables of the problem.
Where:
x = 0.579[m]
y = 1.45 [m]
Using the following kinematic equation we can find the time that takes the water to hit the ground, and then with this time, we can find the velocity of the water in the x-component.
![y = y_{o} +v_{o} *t+\frac{1}{2} *g*t^{2} \\](https://tex.z-dn.net/?f=y%20%3D%20y_%7Bo%7D%20%2Bv_%7Bo%7D%20%2At%2B%5Cfrac%7B1%7D%7B2%7D%20%2Ag%2At%5E%7B2%7D%20%5C%5C)
It is necessary to clarify the value of each of the respective variables below
y = - 1.45 [m] "It is negative because this point is below the water outlet"
yo = 0
vo = 0 "The velocity is zero because the component of the speed on the Y-axis does not exist"
therefore:
![-1.45=0.5*(-9.81)*t^{2} \\t = \sqrt{\frac{1.45}{0.5*9.81} } \\t = 0.543[s]](https://tex.z-dn.net/?f=-1.45%3D0.5%2A%28-9.81%29%2At%5E%7B2%7D%20%5C%5Ct%20%3D%20%5Csqrt%7B%5Cfrac%7B1.45%7D%7B0.5%2A9.81%7D%20%7D%20%5C%5Ct%20%3D%200.543%5Bs%5D)
The next step is to determine the velocity in component x, knowing the time.
![v=\frac{x}{t} \\v=\frac{0.579}{.543} \\v = 1.06[m/s]](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bx%7D%7Bt%7D%20%5C%5Cv%3D%5Cfrac%7B0.579%7D%7B.543%7D%20%5C%5Cv%20%3D%201.06%5Bm%2Fs%5D)
Now using torricelli's law we can find the elevation.
![v=\sqrt{2*g*h} \\h=\frac{v^{2} }{2*g} \\h=\frac{1.06^{2} }{2*9.81} \\h= 0.057[m] = 57.95[mm]](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B2%2Ag%2Ah%7D%20%5C%5Ch%3D%5Cfrac%7Bv%5E%7B2%7D%20%7D%7B2%2Ag%7D%20%5C%5Ch%3D%5Cfrac%7B1.06%5E%7B2%7D%20%7D%7B2%2A9.81%7D%20%5C%5Ch%3D%200.057%5Bm%5D%20%3D%2057.95%5Bmm%5D)
Answer:
A. 1.4 m/s to the left
Explanation:
To solve this problem we must use the principle of conservation of momentum. Let's define the velocity signs according to the direction, if the velocity is to the right, a positive sign will be introduced into the equation, if the velocity is to the left, a negative sign will be introduced into the equation. Two moments will be analyzed in this equation. The moment before the collision and the moment after the collision. The moment before the collision is taken to the left of the equation and the moment after the collision to the right, so we have:
![M_{before} = M_{after}](https://tex.z-dn.net/?f=M_%7Bbefore%7D%20%3D%20M_%7Bafter%7D)
where:
M = momentum [kg*m/s]
M = m*v
where:
m = mass [kg]
v = velocity [m/s]
![(m_{1} *v_{1} )-(m_{2} *v_{2})=(m_{1} *v_{3} )+(m_{2} *v_{4})](https://tex.z-dn.net/?f=%28m_%7B1%7D%20%2Av_%7B1%7D%20%29-%28m_%7B2%7D%20%2Av_%7B2%7D%29%3D%28m_%7B1%7D%20%2Av_%7B3%7D%20%29%2B%28m_%7B2%7D%20%2Av_%7B4%7D%29)
where:
m1 = mass of the basketball = 0.5 [kg]
v1 = velocity of the basketball before the collision = 5 [m/s]
m2 = mass of the tennis ball = 0.05 [kg]
v2 = velocity of the tennis ball before the collision = - 30 [m/s]
v3 = velocity of the basketball after the collision [m/s]
v4 = velocity of the tennis ball after the collision = 34 [m/s]
Now replacing and solving:
(0.5*5) - (0.05*30) = (0.5*v3) + (0.05*34)
1 - (0.05*34) = 0.5*v3
- 0.7 = 0.5*v
v = - 1.4 [m/s]
The negative sign means that the movement is towards left
Whichever one has the greatest gain in speed during that time period has.
If I could see the picture or the rest of the information that goes with that
question, I could tell you exactly which one it is.