Answer:
ω = ω₀ + α t
ω² = ω₀² + 2 α θ
θ = θ₀ + ω₀ t + ½ α t²
Explanation:
Rotational kinematics can be treated as equivalent to linear kinematics, for this change the displacement will change to the angular displacement, the velocity to the angular velocity and the acceleration to the angular relation, that is
x → θ
v → ω
a → α
with these changes the three linear kinematics relations change to
ω = ω₀ + α t
ω² = ω₀² + 2 α θ
θ = θ₀ + ω₀ t + ½ α t²
where it should be clarified that to use these equations the angles must be measured in radians
Answer:
or 0.07163 T into the page
Explanation:
m = Mass of particle = 10 g
a = Acceleration due to gravity = -9.8j m/s²
v = Velocity of particle = 19i km/s
q = Charge of particle = 72 μC
B = Magnetic field
Here the magnetic and gravitational forces on the particle are applied in the opposite direction so,
![F_b=F_g](https://tex.z-dn.net/?f=F_b%3DF_g)
![F_b=qvBsin\theta\\\Rightarrow F_b=qvBsin90\\\Rightarrow F_b=72\times 10^{-6}\times 19000B](https://tex.z-dn.net/?f=F_b%3DqvBsin%5Ctheta%5C%5C%5CRightarrow%20F_b%3DqvBsin90%5C%5C%5CRightarrow%20F_b%3D72%5Ctimes%2010%5E%7B-6%7D%5Ctimes%2019000B)
![F_g=ma\\\Rightarrow F_g=0.01\times -9.8](https://tex.z-dn.net/?f=F_g%3Dma%5C%5C%5CRightarrow%20F_g%3D0.01%5Ctimes%20-9.8)
![72\times 10^{-6}\times 19000B=0.01\times -9.8\\\Rightarrow B=\frac{0.01\times -9.8}{72\times 10^{-6}\times 19000}\\\Rightarrow B=-0.07163\hat k\ T](https://tex.z-dn.net/?f=72%5Ctimes%2010%5E%7B-6%7D%5Ctimes%2019000B%3D0.01%5Ctimes%20-9.8%5C%5C%5CRightarrow%20B%3D%5Cfrac%7B0.01%5Ctimes%20-9.8%7D%7B72%5Ctimes%2010%5E%7B-6%7D%5Ctimes%2019000%7D%5C%5C%5CRightarrow%20B%3D-0.07163%5Chat%20k%5C%20T)
The magnetic field is 0.07163 T into the page
Answer:
The coefficient of kinetic is
![u_{k}=0.59](https://tex.z-dn.net/?f=u_%7Bk%7D%3D0.59)
Explanation:
The forces in the axis 'x' and 'y' using law of Newton to find coefficient of kinetic friction
ΣF=m*a
ΣFy=W-N=0
ΣFy=Fn-Fu=m*a
![F_{u} =u_{k} *N\\F_{N}=25N\\N=W\\N=3.5kg*9.8\frac{m}{s^{2} }=34.3N](https://tex.z-dn.net/?f=F_%7Bu%7D%20%3Du_%7Bk%7D%20%2AN%5C%5CF_%7BN%7D%3D25N%5C%5CN%3DW%5C%5CN%3D3.5kg%2A9.8%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%20%7D%3D34.3N)
![F_{N}-F_{u}=m*a\\F_{N}-u_{k}*N=m*a\\u_{k}*N=F_{N}-m*a\\u_{k}=\frac{F_{N}-m*a}{N}](https://tex.z-dn.net/?f=F_%7BN%7D-F_%7Bu%7D%3Dm%2Aa%5C%5CF_%7BN%7D-u_%7Bk%7D%2AN%3Dm%2Aa%5C%5Cu_%7Bk%7D%2AN%3DF_%7BN%7D-m%2Aa%5C%5Cu_%7Bk%7D%3D%5Cfrac%7BF_%7BN%7D-m%2Aa%7D%7BN%7D)
Now to find the coefficient can find the acceleration using equation of uniform motion accelerated
![v_{f} ^{2}=v_{o}^{2}+2*a(x_{f}-x_{o})\\x_{o}=0\\v_{o}=0\\v_{f} ^{2}=2*a*x_{f}\\a=\frac{v_{f} ^{2}}{2*a*x_{f}}\\ a=\frac{(1.53\frac{m}{s} )^{2}}{2*0.91m}\\a= 1.28 \frac{m}{s^{2} }](https://tex.z-dn.net/?f=v_%7Bf%7D%20%5E%7B2%7D%3Dv_%7Bo%7D%5E%7B2%7D%2B2%2Aa%28x_%7Bf%7D-x_%7Bo%7D%29%5C%5Cx_%7Bo%7D%3D0%5C%5Cv_%7Bo%7D%3D0%5C%5Cv_%7Bf%7D%20%5E%7B2%7D%3D2%2Aa%2Ax_%7Bf%7D%5C%5Ca%3D%5Cfrac%7Bv_%7Bf%7D%20%5E%7B2%7D%7D%7B2%2Aa%2Ax_%7Bf%7D%7D%5C%5C%20a%3D%5Cfrac%7B%281.53%5Cfrac%7Bm%7D%7Bs%7D%20%29%5E%7B2%7D%7D%7B2%2A0.91m%7D%5C%5Ca%3D%201.28%20%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%20%7D)
So replacing the acceleration can fin the coefficient:
![u_{k}=\frac{F_{N}-m*a }{N}\\u_{k}=\frac{25N-(3.5kg*1.28\frac{m}{s^{2}} }{34.3N} \\u_{k}=0.59](https://tex.z-dn.net/?f=u_%7Bk%7D%3D%5Cfrac%7BF_%7BN%7D-m%2Aa%20%7D%7BN%7D%5C%5Cu_%7Bk%7D%3D%5Cfrac%7B25N-%283.5kg%2A1.28%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20%7D%7B34.3N%7D%20%5C%5Cu_%7Bk%7D%3D0.59)
Answer:
Minimum uncertainty in velocity of a proton,
Explanation:
It is given that,
A proton is confined to a space 1 fm wide, ![\Delta x=10^{-15}\ m](https://tex.z-dn.net/?f=%5CDelta%20x%3D10%5E%7B-15%7D%5C%20m)
We need to find the minimum uncertainty in its velocity. We know that the Heisenberg Uncertainty principle gives the uncertainty between position and the momentum such that,
![\Delta p.\Delta x\ge \dfrac{h}{4\pi}](https://tex.z-dn.net/?f=%5CDelta%20p.%5CDelta%20x%5Cge%20%5Cdfrac%7Bh%7D%7B4%5Cpi%7D)
Since, p = mv
![\Delta (mv).\Delta x\ge \dfrac{h}{4\pi}](https://tex.z-dn.net/?f=%5CDelta%20%28mv%29.%5CDelta%20x%5Cge%20%5Cdfrac%7Bh%7D%7B4%5Cpi%7D)
![m \Delta v.\Delta x\ge \dfrac{h}{4\pi}](https://tex.z-dn.net/?f=m%20%5CDelta%20v.%5CDelta%20x%5Cge%20%5Cdfrac%7Bh%7D%7B4%5Cpi%7D)
![\Delta v\ge \dfrac{h}{4\pi m\Delta x}](https://tex.z-dn.net/?f=%5CDelta%20v%5Cge%20%5Cdfrac%7Bh%7D%7B4%5Cpi%20m%5CDelta%20x%7D)
![\Delta v\ge \dfrac{6.63\times 10^{-34}}{4\pi \times 1.67\times 10^{-27}\times 10^{-15}}](https://tex.z-dn.net/?f=%5CDelta%20v%5Cge%20%5Cdfrac%7B6.63%5Ctimes%2010%5E%7B-34%7D%7D%7B4%5Cpi%20%5Ctimes%201.67%5Ctimes%2010%5E%7B-27%7D%5Ctimes%2010%5E%7B-15%7D%7D)
![\Delta v\ge 3.15\times 10^7\ m/s](https://tex.z-dn.net/?f=%5CDelta%20v%5Cge%203.15%5Ctimes%2010%5E7%5C%20m%2Fs)
So, the minimum uncertainty in its velocity is greater than
. Hence, this is the required solution.
<span>
Gravity is pushing you down on the earth while the friction from the ground is pushing you up. Those are the two frictions you must overcome when walking.
</span>