Physics, 10.09.2019 20:30 nefertiri64

Three forces with magnitudes of 66 pounds, 110 pounds, and 138 pounds act on an object at angles of 30°, 45°, and 120° respectively, with the positive x-axis. find the direction and magnitude of the resultant force. (round your answers to one decimal place.)

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Answer from: adrian128383

magnitude = 239.5 lbfdirection ( angle to the x axis) = 74.0

Explanation:

We just need to sum the forces, we can do this easily in their Cartesian form.

Knowing the magnitude and angle with the positive x axis, we can find Cartesian representation of the vectors using the formula

$\vec{A}= |\vec{A}| \ ( \ cos(\theta) \ , \ sin (\theta) \ )$

where $|\vec{A}|$ its the magnitude of the vector and θ the angle with the positive x axis.

So, for our forces we got:

$\vec{F}_1 \ = \ 66 \ lbf \ * \ ( \ cos (30\°)\ , \ sin(30\°) \ )$

$\vec{F}_2 \ = \ 110 \ lbf \ * \ ( \ cos (45\°)\ , \ sin(45\°) \ )$

$\vec{F}_3 \ = \ 138 \ lbf \ * \ ( \ cos (120\°)\ , \ sin(120\°) \ )$

this will give us:

$\vec{F}_1 \ = ( \ 57.157 \ lbf \ , \ 33 \ lbf \ )$

$\vec{F}_2 \ = ( \ 77.782 \ lbf \ , \ 77.782 \ lbf \ )$

$\vec{F}_3 \ = ( \ - 69 \ lbf \ , \ 119.511 \ lbf \ )$

Now, we just sum the forces:

$\vec{F}_{net} \ = \ \vec{F}_1 \ + \ \vec{F}_2 \ + \ \vec{F}_3$

$\vec{F}_{net} \ = ( \ 57.157 \ lbf \ , \ 33 \ lbf \ ) + ( \ 77.782 \ lbf \ , \ 77.782 \ lbf \ ) + (\ - 69 \ lbf \ , \ 119.511 \ lbf \ )$

$\vec{F}_{net} \ = ( \ 57.157 \ lbf \ + \ 77.782 \ lbf \ - \ 69 \ lbf \, \ 33 \ lbf \ + \ 77.782 \ lbf \ + \ 119.511 \ lbf \ )$

$\vec{F}_{net} \ = ( \ 65.939 \ lbf \, \ 230.293 lbf \ )$

This is the net force, to obtain the magnitude, we just need to find the length of the vector, using the Pythagorean formula:

$|\vec{F}_{net}| = \sqrt{(F_{net_x})^2+(F_{net_y})^2}$

$|\vec{F}_{net}| = \sqrt{(65.939 \ lbf)^2+(230.293 lbf)^2}$

$|\vec{F}_{net}| = \ 239.547 \ lbf$

To obtain the angle with the positive x-axis we can use the formula:

$\theta \ = \ arctan( \frac{F_y}{F_y})$

$\theta \ = \ arctan( \frac{230.293 lbf}{65.939 \ lbf})$

$\theta \ = \ arctan( 3.492)$

$\theta \ = \ 74.02$

So, the answer its

$magnitude = \ 239.547 \ lbf$

$angle_{ (to the x axis)} = \ 74.02$

Rounding up:

$magnitude = \ 239.5 \ lbf$

$angle_{ (to the x axis)} = \ 74.0$

Answer from: Quest

carbon is found in all living things. carbon atoms move constantly through

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known as the carbon cycle. the directions taken by carbon atoms through this

cycle are very complicated and can take millions of years to make a full circle.

all animals, from humans to the dinosaurs are part of the carbon cycle. when

animals eat food, they get carbon in the form of carbohydrates and proteins.

in animals, oxygen combines with food in the cells to produce energy for daily

activity and then gives off carbon. the carbon combines with oxygen to form

carbon dioxide (co2) and is released back into the atmosphere as a waste

product when animals breathe and exhale.

from 145-65 million years ago, earth was much

hotter than today and covered with dense,

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plants were immense and

provided an endless supply of

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the air above one of these

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up with two oxygen atoms to form a molecule of co2.

the co2 molecule was sucked into the tiny holes (stomata) on the leaf of a

fern plant and joined with sunlight, chlorophyll and water to make food and

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co2 molecule was sent back into the atmosphere; the carbon atom (c) was

detached and used to make a molecule of sugar.

if that carbon atom had been eaten instead, a totally

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that a giant plant-eating dinosaur (herbivore) ate the

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the process of respiration, oxygen combined with

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to provide energy for its daily activity.

Answer from: Quest

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Three forces with magnitudes of 66 pounds, 110 pounds, and 138 pounds act on an object at angles of...

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