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Ostrovityanka [42]
3 years ago
6

A 1.8 kg uniform rod with a length of 90 cm is attached at one end to a frictionless pivot. It is free to rotate about the pivot

in the vertical plane. The rod is held in the horizontal position and released from rest. What is the initial angular acceleration of the rod and the initial linear acceleration of the right end of the rod?
Physics
1 answer:
Leokris [45]3 years ago
5 0

Answer:

a. 32.67 rad/s²  b. 29.4 m/s²

Explanation:

a. The initial angular acceleration of the rod

Since torque τ = Iα = WL (since the weight of the rod W is the only force acting on the rod , so it gives it a torque, τ at distance L from the pivot )where I = rotational inertia of uniform rod about pivot = mL²/3 (moment of inertia about an axis through one end of the rod), α = initial angular acceleration, W = weight of rod = mg where m = mass of rod = 1.8 kg and g = acceleration due to gravity = 9.8 m/s² and L = length of rod = 90 cm = 0.9 m.

So, Iα = WL

mL²α/3 = mgL

dividing through by mL, we have

Lα/3 = g

multiplying both sides by 3, we have

Lα = 3g

dividing both sides by L, we have

α = 3g/L

Substituting the values of the variables, we have

α = 3g/L

= 3 × 9.8 m/s²/0.9 m

= 29.4/0.9 rad/s²

= 32.67 rad/s²

b. The initial linear acceleration of the right end of the rod?

The linear acceleration at the initial point is tangential, so a = Lα = 0.9 m × 32.67 rad/s² = 29.4 m/s²

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)If a force of 5.00 N is needed to open a 90.0 cm wide door when applied at the edge opposite the hinges, what force must be app
masha68 [24]

Answer:

A force of 12.857 newtons must be applied to open the door.

Explanation:

In this case, a force is exerted on the door, a moment is performed and the door is opened. If moment remains constant, the force is inversely proportional to distance respect to axis of rotation passing through hinges. That is:

F \propto \frac{1}{r}

F = \frac{k}{r} (Eq. 1)

Where:

F - Force, measured in newtons.

k - Proportionality ratio, measured in newton-meters.

r - Distance respect to axis of rotation passing through hinges, measured in meters.

From (Eq. 1) we get the following relationship and clear the final force within:

F_{A}\cdot r_{A} = F_{B}\cdot r_{B}

F_{B}=\left(\frac{r_{A}}{r_{B}} \right)\cdot F_{A}(Eq. 2)

Where:

F_{A}, F_{B} - Initial and final forces, measured in newtons.

r_{A}, r_{B} - Initial and final distances, measured in meters.

If we know that F_{A} = 5\,N, r_{A} = 0.9\,m and r_{B} = 0.35\,m, then final force is:

F_{B}= \left(\frac{0.9\,m}{0.35\,m} \right)\cdot (5\,N)

F_{B} = 12.857\,N

A force of 12.857 newtons must be applied to open the door.

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Answer:

The  value is   \alpha =  0.002 Np/m

Explanation:

From the question we are told that

  The first amplitude of the wave is  E_{max}1 =  98.02 \  V/m

  The first  depth  is  D_1 =  10 \  m

   The second amplitude is  E_{max}2 =  81.87 \  (V/m)

   The second depth is D_2 = 100 \ m

Generally from the spatial wave equation we have

   v(x) =  Ae^{-\alpha d}cos(\beta x  + \phi_o)

=>       \frac{v(x)}{v(x)} =\frac{  Ae^{-\alpha d}cos(\beta x  + \phi_o)}{ Ae^{-\alpha d}cos(\beta x  + \phi_o)}

So considering the ratio of the equation for the  two depth

\frac{A}{A_S}  =  \frac{e^{-D_1 \alpha }}{e^{-D_2 \alpha }}

=>   \frac{98.02}{81.87}  =  \frac{e^{-10 \alpha }}{e^{-100 \alpha }}

=>   \alpha  =  \frac{0.18}{90}

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4 0
3 years ago
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aleksklad [387]

Answer:

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By triangle addition of vector

B=A+C

C=B-A

C_x=B_x-A_x=32.5-17=15.5 m

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\mid C\mid=\sqrt{C^2_x+C^2_y}

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6 0
3 years ago
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