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Pavlova-9 [17]
3 years ago
15

A 4.00-m long rod is hinged at one end. The rod is initially held in the horizontal position, and then released as the free end

is allowed to fall. What is the angular acceleration as it is released
Physics
1 answer:
Natalka [10]3 years ago
5 0

Answer:

The angular acceleration α = 14.7 rad/s²

Explanation:

The torque on the rod τ = Iα where I = moment of inertia of rod = mL²/12 where m =mass of rod  and L = length of rod = 4.00 m. α = angular acceleration of rod

Also, τ = Wr where W = weight of rod = mg and r = center of mass of rod = L/2.

So Iα = Wr

Substituting the value of the variables, we have

mL²α/12 = mgL/2

Simplifying by dividing through by mL, we have

mL²α/12mL = mgL/2mL

Lα/12 = g/2

multiplying both sides by 12, we have

Lα/12 × 12 = g/2 × 12

αL = 6g

α = 6g/L

α = 6 × 9.8 m/s² ÷ 4.00 m

α = 58.8 m/s² ÷ 4.00 m

α = 14.7 rad/s²

So, the angular acceleration α = 14.7 rad/s²

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Answer:

1.6675×10^-16N

Explanation:

The force of gravity that the space shuttle experiences is expressed as;

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Substitute into the formula

g = 6.67×10^-11 × 1.0×10^5/(2×10^5)²

g = 6.67×10^-6/4×10^10

g = 1.6675×10^{-6-10}

g = 1.6675×10^-16N

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7 0
3 years ago
What happens to the acceleration of an object if the net force that acts on it triples in magnitude?
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F=ma Force is equal to mass times acceleration.


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5 0
4 years ago
A 16.0 m long, thin, uniform metal rod slides north at a speed of 21.0 m/s. The length of the rod maintains an east-west orienta
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Answer:

14.112 mV

Explanation:

L = 16 m, v = 21 m/s, B = 42 μ T = 42 x 10^-6 T

The formula for the induced emf is given by

e = B x v x L

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Thus, the induce emf is 14.112 mV.

4 0
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For no apparent reason, a poodle is running at a constant speed of 5.00 m/s in a circle with radius 2.9 m . Let v⃗ 1 be the velo
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At a constant speed of 5.00 m/s, the speed at which the poodle completes a full revolution is

\left(5.00\,\dfrac{\mathrm m}{\mathrm s}\right)\left(\dfrac{1\,\mathrm{rev}}{2\pi(2.9\,\mathrm m)}\right)\approx0.2744\,\dfrac{\mathrm{rev}}{\mathrm s}

so that its period is T=3.644\,\frac{\mathrm s}{\mathrm{rev}} (where 1 revolution corresponds exactly to 360 degrees). We use this to determine how much of the circular path the poodle traverses in each given time interval with duration \Delta t. Denote by \theta the angle between the velocity vectors (same as the angle subtended by the arc the poodle traverses), then

\Delta t=0.4\,\mathrm s\implies\dfrac{3.644\,\mathrm s}{360^\circ}=\dfrac{0.4\,\mathrm s}\theta\implies\theta\approx39.56^\circ

\Delta t=0.2\,\mathrm s\implies\dfrac{3.644\,\mathrm s}{360^\circ}=\dfrac{0.2\,\mathrm s}\theta\implies\theta\approx19.78^\circ

\Delta t=7\times10^{-2}\,\mathrm s\implies\dfrac{3.644\,\mathrm s}{360^\circ}=\dfrac{7\times10^{-2}\,\mathrm s}\theta\implies\theta\approx6.923^\circ

We can then compute the magnitude of the velocity vector differences \Delta\vec v for each time interval by using the law of cosines:

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and in turn we find the magnitude of the average acceleration vectors to be

\implies|\vec a|=\begin{cases}8.460\,\frac{\mathrm m}{\mathrm s^2}&\text{for }\Delta t=0.4\,\mathrm s\\8.588\,\frac{\mathrm m}{\mathrm s^2}&\text{for }\Delta t=0.2\,\mathrm s\\8.625\,\frac{\mathrm m}{\mathrm s^2}&\text{for }\Delta t=7\times10^{-2}\,\mathrm s\end{cases}

So that takes care of parts A, C, and E. Unfortunately, without knowing the poodle's starting position, it's impossible to tell precisely in what directions each average acceleration vector points.

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