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Salsk061 [2.6K]
3 years ago
6

The force of magnitude F acts along the edge of the triangular plate. Determine the moment of F about point O. Find the general

result and then evaluate your answer if F = 260 N, b = 580 mm, and h = 370 mm. The moment is positive if counterclockwise, negative if clockwise.

Physics
1 answer:
Sever21 [200]3 years ago
5 0

Answer:

The moment is 81.102 k N-m in clockwise.

Explanation:

Given that,

Force = 260 N

Side = 580 mm

Distance h = 370 mm

According to figure,

Position of each point

O=(0,0)

A=(0,-b)

B=(h,0)

We need to calculate the position vector of AB

\bar{AB}=(h-0)i+(0-(-b))j

\bar{AB}=hi+bj

We need to calculate the unit vector along AB

u_{AB}=\dfrac{\bar{AB}}{|\bar{AB}|}

u_{AB}=\dfrac{h\hat{i}+b\hat{j}}{\sqrt{h^2+b^2}}

We need to calculate the force acting along the edge

\hat{F}=F(u_{AB})

\hat{F}=F(\dfrac{h\hat{i}+b\hat{j}}{\sqrt{h^2+b^2}})

We need to calculate the net moment

\hat{M}=\hat{F}\times OA

Put the value into the formula

\hat{M}=F(\dfrac{h\hat{i}+b\hat{j}}{\sqrt{h^2+b^2}})\times(-b\hat{j})

\hat{M}=\dfrac{F}{\sqrt{h^2+b^2}}((h\hat{i}+b\hat{j})\times(-b\hat{j}))

\hat{M}=\dfrac{F}{\sqrt{h^2+b^2}}(-bh\hat{k})

\hat{M}=-\dfrac{bhF}{\sqrt{h^2+b^2}}

Put the value into the formula

\hat{M}=-\dfrac{580\times10^{-3}\times370\times10^{-3}\times260}{\sqrt{(370\times10^{-3})^2+(580\times10^{-3})^2}}

\hat{M}=-81.102\ \hat{k}\ N-m

Negative sign shows the moment is in clockwise.

Hence, The moment is 81.102 k N-m in clockwise.

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Fn₃= 810 N

Explanation:

Look at the attached graphic:

The charges of the same sign exert forces of repulsion and the charges of   opposite sign exert forces of attraction.

Each of the charges experiences 2 forces and these forces are equal and we calculate them with Coulomb's law:

F= (k*q*q)/(d)²

F= (9*10⁹*3*10⁻⁶*3*10⁻⁶)(0.01)² =810N

Magnitude of the net force on q₁-

Fn₁x= 0

Fn₁y= 2*F*sin60 = 2*810*sin60° = 1403 N

Fn₁=1403 N

Magnitude of the net force on q₃+

Fn₃x= 810- 810 cos 60° = 405 N

Fn₃y= 810*sin 60° = 701.5 N

Fn_{3} = \sqrt{405^{2}+701.5^{2}  }

Fn₃ = 810 N

Magnitude of the net force on q₂+

Fn₂ = Fn₃ = 810 N

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3 years ago
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a 0.0780 kg lemming runs off a 5.36 m high cliff at 4.84 m/s. what is its kinetic energy when it's 2.00 m above the ground
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4.10J+0.914J = 1.53J + KE_2

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KE_2 = 3.48J

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6 0
2 years ago
A distance of 200 ft must be taped in a manner to ensure a standard deviation smaller than ± 0.04 ft. What must be the standard
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Answer:

The error in tapping is ±0.02828 ft.

Explanation:

Given that,

Distance = 200 ft

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We need to calculate the error in tapping

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E=\dfrac{E_{series}}{\sqrt{n}}

Put the value into the formula

E=\dfrac{0.04}{\sqrt{2}}

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Hence, The error in tapping is ±0.02828 ft.

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