Answer:
The mass of the another block is 60 kg.
Explanation:
Given that,
Mass of block M= 100 kg
Height = 1.0 m
Time = 0.90 s
Let the mass of the other block is m.
We need to calculate the acceleration of each block
Using equation of motion
![s=ut+\dfrac{1}{2}at^2](https://tex.z-dn.net/?f=s%3Dut%2B%5Cdfrac%7B1%7D%7B2%7Dat%5E2)
Put the value into the formula
![1.0=0+\dfrac{1}{2}\times a\times(0.90)^2](https://tex.z-dn.net/?f=1.0%3D0%2B%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20a%5Ctimes%280.90%29%5E2)
![a=\dfrac{2\times1.0}{(0.90)^2}](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7B2%5Ctimes1.0%7D%7B%280.90%29%5E2%7D)
![a=2.46\ m/s^2](https://tex.z-dn.net/?f=a%3D2.46%5C%20m%2Fs%5E2)
We need to calculate the mass of the other block
Using newton's second law
The net force of the block M
![Ma=Mg-T](https://tex.z-dn.net/?f=Ma%3DMg-T)
....(I)
The net force of the block m
![ma=T-mg](https://tex.z-dn.net/?f=ma%3DT-mg)
Put the value of T from equation (I)
![ma=Mg-Ma-mg](https://tex.z-dn.net/?f=ma%3DMg-Ma-mg)
![m(a+g)=M(g-a)](https://tex.z-dn.net/?f=m%28a%2Bg%29%3DM%28g-a%29)
![m=\dfrac{M(g-a)}{(a+g)}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7BM%28g-a%29%7D%7B%28a%2Bg%29%7D)
Put the value into the formula
![m=\dfrac{100(9.8-2.46)}{2.46+9.8}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B100%289.8-2.46%29%7D%7B2.46%2B9.8%7D)
![m=59.8\ \approx60\ kg](https://tex.z-dn.net/?f=m%3D59.8%5C%20%5Capprox60%5C%20kg)
Hence, The mass of the another block is 60 kg.
Because acceleration is constant, the acceleration of the car at any time is the same as its average acceleration over the duration. So
![a=\dfrac{\Delta v}{\Delta t}=\dfrac{46.1\,\frac{\mathrm m}{\mathrm s}-18.5\,\frac{\mathrm m}{\mathrm s}}{2.47\,\mathrm s}=11.2\,\dfrac{\mathrm m}{\mathrm s^2}](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7B%5CDelta%20v%7D%7B%5CDelta%20t%7D%3D%5Cdfrac%7B46.1%5C%2C%5Cfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%7D-18.5%5C%2C%5Cfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%7D%7D%7B2.47%5C%2C%5Cmathrm%20s%7D%3D11.2%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%5E2%7D)
Now, we have that
![{v_f}^2-{v_0}^2=2a\Delta x](https://tex.z-dn.net/?f=%7Bv_f%7D%5E2-%7Bv_0%7D%5E2%3D2a%5CDelta%20x)
so we end up with a distance traveled of
![\left(46.1\,\dfrac{\mathrm m}{\mathrm s}\right)^2-\left(18.5\,\dfrac{\mathrm m}{\mathrm s}\right)^2=2\left(11.2\,\dfrac{\mathrm m}{\mathrm s^2}\right)\Delta x](https://tex.z-dn.net/?f=%5Cleft%2846.1%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%7D%5Cright%29%5E2-%5Cleft%2818.5%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%7D%5Cright%29%5E2%3D2%5Cleft%2811.2%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29%5CDelta%20x)
![\implies\Delta x=79.6\,\mathrm m](https://tex.z-dn.net/?f=%5Cimplies%5CDelta%20x%3D79.6%5C%2C%5Cmathrm%20m)
Answer:
This is known as a Galilean transformation where
V' = V - U
Where the primed frame is the Earth frame and the unprimed frame is the frame moving with respect to the moving frame
V - speed of object in the unprimed frame
U - speed of primed frame with respect to the unprimed frame
Here we have:
V = -15 m/s speed of ball in the moving frame (the truck)
U = -20 m/s speed of primed (rest) frame with respect to moving frame
So V' = -15 - (-20) = 5 m/s
It may help if you draw a vector representing the moving frame and then add
a vector representing the speed of the ball in the moving frame.
Answer:
When the volume increases or when the temperature decreases
Explanation:
The ideal gas equation states that:
![pV= nRT](https://tex.z-dn.net/?f=pV%3D%20nRT)
where
p is the gas pressure
V is the volume
n is the number of moles of gas
R is the gas constant
T is the gas temperature
Assuming that we have a fixed amount of gas, so n is constant, we can rewrite the equation as
![\frac{pV}{T}=const.](https://tex.z-dn.net/?f=%5Cfrac%7BpV%7D%7BT%7D%3Dconst.)
which means the following:
- Pressure is inversely proportional to the volume: this means that the pressure decreases when the volume increases
- Pressure is directly proportional to the temperature: this means that the pressure decreases when the temperature decreases
This attraction occurs from adhesion, also known as adsorption <span />