Answer:
0.88752 kgm²
0.02236 Nm
Explanation:
m = Mass of ball = 1.2 kg
L = Length of rod = 0.86 m
= Angle = 90°
Rotational inertia is given by
![I=mL^2\\\Rightarrow I=1.2\times 0.86^2\\\Rightarrow I=0.88752\ kgm^2](https://tex.z-dn.net/?f=I%3DmL%5E2%5C%5C%5CRightarrow%20I%3D1.2%5Ctimes%200.86%5E2%5C%5C%5CRightarrow%20I%3D0.88752%5C%20kgm%5E2)
The rotational inertia is 0.88752 kgm²
Torque is given by
![\tau=FLsin\theta\\\Rightarrow \tau=2.6\times 10^{-2}\times 0.86sin90\\\Rightarrow \tau=0.02236\ Nm](https://tex.z-dn.net/?f=%5Ctau%3DFLsin%5Ctheta%5C%5C%5CRightarrow%20%5Ctau%3D2.6%5Ctimes%2010%5E%7B-2%7D%5Ctimes%200.86sin90%5C%5C%5CRightarrow%20%5Ctau%3D0.02236%5C%20Nm)
The torque is 0.02236 Nm
The car has an initial velocity
of 23 m/s and a final velocity
of 0 m/s. Recall that for constant acceleration,
![v=v_0+at](https://tex.z-dn.net/?f=v%3Dv_0%2Bat)
The car stops in 7 s, so the acceleration is
![0\,\dfrac{\mathrm m}{\mathrm s}=23\,\dfrac{\mathrm m}{\mathrm s}+a(7\,\mathrm s)](https://tex.z-dn.net/?f=0%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%7D%3D23%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%7D%2Ba%287%5C%2C%5Cmathrm%20s%29)
![\implies a\approx-3.29\,\dfrac{\mathrm m}{\mathrm s^2}](https://tex.z-dn.net/?f=%5Cimplies%20a%5Capprox-3.29%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%5E2%7D)
Answer:
Explanation:
Given
Diameter of Pulley=10.4 cm
mass of Pulley(m)=2.3 kg
mass of book![(m_0)=1.7 kg](https://tex.z-dn.net/?f=%28m_0%29%3D1.7%20kg)
height(h)=1 m
time taken=0.64 s
![h=ut+frac{at^2}{2}](https://tex.z-dn.net/?f=h%3Dut%2Bfrac%7Bat%5E2%7D%7B2%7D)
![1=0+\frac{a(0.64)^2}{2}](https://tex.z-dn.net/?f=1%3D0%2B%5Cfrac%7Ba%280.64%29%5E2%7D%7B2%7D)
![a=4.88 m/s^2and [tex]a=\alpha r](https://tex.z-dn.net/?f=a%3D4.88%20m%2Fs%5E2%3C%2Fp%3E%3Cp%3Eand%20%5Btex%5Da%3D%5Calpha%20r)
where
is angular acceleration of pulley
![4.88=\alpha \times 5.2\times 10^{-2}](https://tex.z-dn.net/?f=4.88%3D%5Calpha%20%5Ctimes%205.2%5Ctimes%2010%5E%7B-2%7D)
![\alpha =93.84 rad/s^2](https://tex.z-dn.net/?f=%5Calpha%20%3D93.84%20rad%2Fs%5E2)
And Tension in Rope
![T=m(g-a)](https://tex.z-dn.net/?f=T%3Dm%28g-a%29)
![T=1.7\times (9.8-4.88)](https://tex.z-dn.net/?f=T%3D1.7%5Ctimes%20%289.8-4.88%29)
T=8.364 N
and Tension will provide Torque
![T\times r=I\cdot \alpha](https://tex.z-dn.net/?f=T%5Ctimes%20r%3DI%5Ccdot%20%5Calpha%20)
![8.364\times 5.2\times 10^{-2}=I\times 93.84](https://tex.z-dn.net/?f=8.364%5Ctimes%205.2%5Ctimes%2010%5E%7B-2%7D%3DI%5Ctimes%2093.84)
![I=0.463\times 10^{-2} kg-m^2](https://tex.z-dn.net/?f=I%3D0.463%5Ctimes%2010%5E%7B-2%7D%20kg-m%5E2)
![I_{original}=\frac{mr^2}{2}=0.31\times 10^{-2}kg-m^2](https://tex.z-dn.net/?f=I_%7Boriginal%7D%3D%5Cfrac%7Bmr%5E2%7D%7B2%7D%3D0.31%5Ctimes%2010%5E%7B-2%7Dkg-m%5E2)
Thus mass is uniformly distributed or some more towards periphery of Pulley
Answer:
a) ![t=195.948N.m](https://tex.z-dn.net/?f=t%3D195.948N.m)
b) ![\phi=13.6 \textdegree](https://tex.z-dn.net/?f=%5Cphi%3D13.6%20%5Ctextdegree)
Explanation:
From the question we are told that:
Density ![\rho=1.225kg/m^2](https://tex.z-dn.net/?f=%5Crho%3D1.225kg%2Fm%5E2)
Velocity of wind ![v=14m/s](https://tex.z-dn.net/?f=v%3D14m%2Fs)
Dimension of rectangle:50 cm wide and 90 cm
Drag coefficient ![\mu=2.05](https://tex.z-dn.net/?f=%5Cmu%3D2.05)
a)
Generally the equation for Force is mathematically given by
![F=\frac{1}{2}\muA\rhov^2](https://tex.z-dn.net/?f=F%3D%5Cfrac%7B1%7D%7B2%7D%5CmuA%5Crhov%5E2)
![F=\frac{1}{2}2.05(50*90*\frac{1}{10000})*1.225*17^2](https://tex.z-dn.net/?f=F%3D%5Cfrac%7B1%7D%7B2%7D2.05%2850%2A90%2A%5Cfrac%7B1%7D%7B10000%7D%29%2A1.225%2A17%5E2)
![F=163.29](https://tex.z-dn.net/?f=F%3D163.29)
Therefore Torque
![t=F*r*sin\theta](https://tex.z-dn.net/?f=t%3DF%2Ar%2Asin%5Ctheta)
![t=163.29*1.2*sin90](https://tex.z-dn.net/?f=t%3D163.29%2A1.2%2Asin90)
![t=195.948N.m](https://tex.z-dn.net/?f=t%3D195.948N.m)
b)
Generally the equation for torque due to weight is mathematically given by
![t=d*Mg*sin90](https://tex.z-dn.net/?f=t%3Dd%2AMg%2Asin90)
Where
![d=sin \phi](https://tex.z-dn.net/?f=d%3Dsin%20%5Cphi)
Therefore
![t=sin \phi*Mg*sin90](https://tex.z-dn.net/?f=t%3Dsin%20%5Cphi%2AMg%2Asin90)
![195.948=833sin \phi](https://tex.z-dn.net/?f=195.948%3D833sin%20%5Cphi)
![\phi=sin^{-1}\frac{195.948}{833}](https://tex.z-dn.net/?f=%5Cphi%3Dsin%5E%7B-1%7D%5Cfrac%7B195.948%7D%7B833%7D)
![\phi=13.6 \textdegree](https://tex.z-dn.net/?f=%5Cphi%3D13.6%20%5Ctextdegree)