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marshall27 [118]
3 years ago
6

A pendulum is transported from sea-level, where the acceleration due to gravity g is 9.80 m/s2, to the bottom of Death Valley. A

t this location, the period of the pendulum is decreased by 3.00%. What is the value of g in Death Valley
Physics
1 answer:
tatyana61 [14]3 years ago
7 0

Answer: the value of g in Death Valley is 10.417 m/s²

Explanation:

Given that;

acceleration due to gravity at the point is g = 9.8 m/s²

Lets say the acceleration due to gravity at the bottom of Death valley is g'

as the period of the pendulum is decreased by 3.00%

T' = 0.97 T  

T is the period of the pendulum at sea level  and T' is the period of the pendulum at bottom of Death valley

therefore from the relation

T = 2π√(l/g)

g'/g = T²/T'²

g' = (T²/ (0.97T)²)g

g' = 1.063g

g' = 10.417 m/s²

therefore the value of g in Death Valley is 10.417 m/s²

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if vector u has lenght 70 and direction 40 degrees, and vector v has length 85 and direction 335 degrees what is the length and
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Magnitude of resultant = 131.15

Direction of resultant = 3.97°

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||v|| = 85

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\vec{v}_x=||v||cos\theta \\\Rightarrow \vec{v}_x=85cos335=77.03

\vec{v}_y=||v||sin\theta \\\Rightarrow \vec{v}_y=85sin335=-35.92

Resultant

R=\sqrt{R_x^2+R_y^2}\\\Rightarrow R=\sqrt{(\vec{u}_x+\vec{v}_x)^2+(\vec{u}_y+\vec{v}_y)^2}\\\Rightarrow R =\sqrt{(70cos40+85cos335)^2+(70sin40+85sin335)^2}\\\Rightarrow R =131.15

\theta=tan^{-1}\frac{R_y}{R_x}\\\Rightarrow \theta=tan^{-1}\frac{70sin40+85sin335}{70cos40+85cos335}\\\Rightarrow \theta=tan^{-1}0.069=3.97^{\circ}

Magnitude of resultant = 131.15

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