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densk [106]
3 years ago
7

A uniform rod of mass M and length L can pivot freely at one end. Initially, the rod is oriented vertically above the pivot, in

unstable equilibrium, and is released from rest. When the rod is again vertical, below the pivot, what is the speed of its center of mass (in terms of g and L)? The rotational inertia about the end of a uniform rod is 1 3 M L2 .
Physics
1 answer:
Leya [2.2K]3 years ago
4 0

Answer:

The speed of its center of mass =\sqrt{\frac{3}{2}gL}

Explanation:

Consider the potential energy at the level of center of mass of rod below the pivot=0

Mass of uniform rod=M

Length of rod=L

The rotational inertia about the end of a uniform rod=\frac{1}{3}ML^2

Kinetic energy at the level of center of mass of rod below the pivot=\frac{1}{2}I\omega^2

Kinetic energy at the level of center of mass of rod above the pivot=0

Potential energy at the level of center of mass of rod above the pivot=mgh

We have to find the center of mass ( in terms of g and L).

According to conservation of law of energy

Initial P.E+Initial K.E=Final P.E+Final K.E

mgh+0=0+\frac{1}{2} I\omega^2

Where K.E=\frac{1}{2} I\omega^2

I=Moment of inertia

\omega=Angular velocity

Substitute the values then we get

MgL=\frac{1}{2}\times \frac{1}{3}ML^2\omega^2

\omega^2=\frac{6g}{L}

Now, we know that \omega=\frac{v}{r}, r=\frac{L}{2}

Substitute the values then we get

\frac{v^2}{(\frac{L}{2})^2}=\frac{6g}{L}

\frac{v^24}{L^2}=\frac{6g}{L}

v^2=\frac{6g\times L^2}{4L}

v^2=\frac{3gL}{2}

v=\sqrt{\frac{3}{2}gL}

Hence, the speed of its center of mass =\sqrt{\frac{3}{2}gL}

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First we need to find the acceleration of the skier on the rough patch of snow.
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a=-(0.220)(9.81 m/s^2)=-2.16 m/s^2

Now we can use the following relationship to find the distance covered by the skier before stopping, S:
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Using newtons second law of motion, how fast for 100 KG object accelerates 350 N of force is applied to
fenix001 [56]

Answer:

3.5m/s^2

Explanation:

From Newton's second Law of Motion

F = ma

Where F is the applied force, m is the mass of the object and a is the acceleration.

F = 350 N

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350N = 100×a

a = 350/100

a = 3.5m/s^2

The acceleration of the object will be 3.5m/s^2

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lilavasa [31]

Answer:

Mutual inductance, M=2.28\times 10^{-5}\ H

Explanation:

(a) A toroidal solenoid with mean radius r and cross-sectional area A is wound uniformly with N₁ turns. A second thyroidal solenoid with N₂ turns is wound uniformly on top of the first, so that the two solenoids have the same cross-sectional area and mean radius.

Mutual inductance is given by :

M=\dfrac{\mu_oN_1N_2A}{2\pi r}

(b) It is given that,

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N_2=290

Radius, r = 10.6 cm = 0.106 m

Area of toroid, A=0.76\ cm^2=7.6\times 10^{-5}\ m^2

Mutual inductance, M=\dfrac{4\pi \times 10^{-7}\times 550\times 290\times 7.6\times 10^{-5}}{2\pi \times 0.106}

M=0.0000228\ H

or

M=2.28\times 10^{-5}\ H

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