Answer:
The trains mass in pounds would be 40084.029 if you would round it to the hundreths
Explanation:
Adding thermal energy
Performing work on the system
Answer:
The distance by the ball clear the crossbar is 1.15 m
Explanation:
Given that,
Distance = 44 m
Speed = 24 m/s
Angle = 31°
Height = 3.05 m
We need to calculate the horizontal velocity
Using formula of horizontal velocity
![u_{x}=u\cos\theta](https://tex.z-dn.net/?f=u_%7Bx%7D%3Du%5Ccos%5Ctheta)
Put the value into the formula
![u_{x}=24\cos(31)](https://tex.z-dn.net/?f=u_%7Bx%7D%3D24%5Ccos%2831%29)
![u_{x}=20.5\ m/s](https://tex.z-dn.net/?f=u_%7Bx%7D%3D20.5%5C%20m%2Fs)
We need to calculate the vertical velocity
Using formula of vertical velocity
![u_{y}=u\sin\theta](https://tex.z-dn.net/?f=u_%7By%7D%3Du%5Csin%5Ctheta)
Put the value into the formula
![u_{y}=24\sin(31)](https://tex.z-dn.net/?f=u_%7By%7D%3D24%5Csin%2831%29)
![u_{y}=12.3\ m/s](https://tex.z-dn.net/?f=u_%7By%7D%3D12.3%5C%20m%2Fs)
We need to calculate the time
Using formula of time
![t=\dfrac{d}{u_{x}}](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7Bd%7D%7Bu_%7Bx%7D%7D)
Put the value into the formula
![t=\dfrac{44}{20.5}](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7B44%7D%7B20.5%7D)
![t=2.1\ sec](https://tex.z-dn.net/?f=t%3D2.1%5C%20sec)
We need to calculate the vertical height
Using equation of motion
![h=u_{y}t+\dfrac{1}{2}at^2](https://tex.z-dn.net/?f=h%3Du_%7By%7Dt%2B%5Cdfrac%7B1%7D%7B2%7Dat%5E2)
Put the value into the formula
![h=12.3\times2.1-\dfrac{1}{2}\times9.8\times(2.1)^2](https://tex.z-dn.net/?f=h%3D12.3%5Ctimes2.1-%5Cdfrac%7B1%7D%7B2%7D%5Ctimes9.8%5Ctimes%282.1%29%5E2)
![h=4.2\ m](https://tex.z-dn.net/?f=h%3D4.2%5C%20m)
We need to calculate the distance by the ball clear the crossbar
Using formula for vertical distance
![d=h-3.05](https://tex.z-dn.net/?f=d%3Dh-3.05)
Put the value of h
![d=4.2-3.05](https://tex.z-dn.net/?f=d%3D4.2-3.05)
![d=1.15\ m](https://tex.z-dn.net/?f=d%3D1.15%5C%20m)
Hence, The distance by the ball clear the crossbar is 1.15 m
Answer
given,
length of slender rod =80 cm = 0.8 m
mass of rod = 0.39 Kg
mass of small sphere = 0.0200 kg
mass of another sphere weld = 0.0500 Kg
calculating the moment of inertia of the system
![I = \dfrac{ML^2}{12}+\dfrac{m_1L^2}{4}+\dfrac{mL^2}{4}](https://tex.z-dn.net/?f=I%20%3D%20%5Cdfrac%7BML%5E2%7D%7B12%7D%2B%5Cdfrac%7Bm_1L%5E2%7D%7B4%7D%2B%5Cdfrac%7BmL%5E2%7D%7B4%7D)
![I = \dfrac{0.39\times 0.8^2}{12}+\dfrac{0.02\times 0.8^2}{4}+\dfrac{0.05\times 0.8^2}{4}](https://tex.z-dn.net/?f=I%20%3D%20%5Cdfrac%7B0.39%5Ctimes%200.8%5E2%7D%7B12%7D%2B%5Cdfrac%7B0.02%5Ctimes%200.8%5E2%7D%7B4%7D%2B%5Cdfrac%7B0.05%5Ctimes%200.8%5E2%7D%7B4%7D)
![I =0.032\ kg.m^2](https://tex.z-dn.net/?f=I%20%3D0.032%5C%20kg.m%5E2)
using conservation of energy
![\dfrac{1}{2}I\omega^2 = (m_1-m_2)g\dfrac{L}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7DI%5Comega%5E2%20%3D%20%28m_1-m_2%29g%5Cdfrac%7BL%7D%7B2%7D)
![\omega=\sqrt{\dfrac{(m_1-m_2)gL}{I}}](https://tex.z-dn.net/?f=%5Comega%3D%5Csqrt%7B%5Cdfrac%7B%28m_1-m_2%29gL%7D%7BI%7D%7D)
![\omega=\sqrt{\dfrac{(0.05-0.02)\times 9.8 \times 0.8}{0.032}}](https://tex.z-dn.net/?f=%5Comega%3D%5Csqrt%7B%5Cdfrac%7B%280.05-0.02%29%5Ctimes%209.8%20%5Ctimes%200.8%7D%7B0.032%7D%7D)
![\omega=2.71 \rad/s](https://tex.z-dn.net/?f=%5Comega%3D2.71%20%5Crad%2Fs)
we know,
v = r ω
![v = \dfrac{L}{2} \times 2.71](https://tex.z-dn.net/?f=v%20%3D%20%5Cdfrac%7BL%7D%7B2%7D%20%5Ctimes%202.71)
![v = \dfrac{0.8}{2} \times 2.71](https://tex.z-dn.net/?f=v%20%3D%20%5Cdfrac%7B0.8%7D%7B2%7D%20%5Ctimes%202.71)
v = 1.084 m/s
Answer:a goal is scored by throwing the ball into the goal post and is confirmed by deciding that’s if the ball has hit the tape mark or not
Explanation: