Three children are struggling and pulling on a single toy. Two of the children, Abe and Barry, are EACH (individually) pulling with a force of 60 Newtons. The third child, Eric, is pulling with enough force to exactly balance Abe and Barry (no child is winning the tug-o-war for the toy). We can label our forces A, B, and E (from each child's name). These three forces are in equilibrium.

If Abe is pulling toward the North and Barry is pulling toward the East, we want to find the total force R due to Abe and Barry (the Resultant of their forces). Note: in THIS case the two forces and R form a right-triangle (with R as the hypotenuse) - as seen using graphical vector addition. As a convention let's have NORTH upward and EAST rightward on this page.

a. Sketch an ACCURATE free-body diagram (three arrows outward from a point showing LABELED forces A, B, and E - each arrow a reasonable length and correct direction):
b. Sketch a labeled diagram for graphical addition of A and B to get R:
c. Show the calculation of the magnitude of R from the magnitudes of A and B:
d. Give the magnitude of force E (in units of Newtons):
e. Describe the direction of force E in terms of the "cardinal" directions (north, east, south, and/or west):

Solution :

c). [tex]$\vec{F}_A = $[/tex] force applied by Abe

   [tex]$\vec{F}_B = $[/tex] force applied by Barry

   [tex]$\vec{F}_E = $[/tex] force applied by Eric

   [tex]$\vec{F}_R = $[/tex] Resultant force

[tex]$\vec{F}_A $[/tex]  in the vector form can be written as :

         [tex]$\vec{F}_A = 0 \hat{i} + 60 \hat{j}$[/tex]

[tex]$\vec{F}_B $[/tex]  in the vector form can be written as :

         [tex]$\vec{F}_B = 60 \hat{i} + 0 \hat{j}$[/tex]

The resultant,

[tex]$\vec{F}_R= \vec{F}_A+\vec{F}_B $[/tex]

     [tex]$=(0 \hat i + 60 \hat j)+(60 \hat i + 0\hat j)$[/tex]

    [tex]$=60 \hat i + 60 \hat j$[/tex]

[tex]$|\vec{F}_R| = \sqrt{60^2+60^2}$[/tex]

        = 84.853 N

d). As the three forces are in equilibrium, therefore,

[tex]$|\vec F_E| = |\vec F_R|$[/tex]

[tex]$|\vec F_E| =84.853 \ N$[/tex]

e). The direction of the force exerted by Eric is exactly opposite to the direction of the resultant force.

The direction of the resultant force is :

[tex]$\theta = \tan ^{-1}\left(\frac{F_y}{F_x}\right)$[/tex]

   [tex]$ = \tan ^{-1}\left(\frac{60}{60}\right)$[/tex]

  = 45°  north east

The direction of the force E is  45° west or  45° south west.

A piece of paper floats though the air towards the ground. At one point, the air resistance (Fair) on the
paper pushes up with 0.01 N of force. Force due to gravity (Fg) pulls the ball down with a force of 0.02 N.
Show your work

The person kicks the ball in the image below 20 meters. Suppose the soccer ball in the image is replaced by one that is twice the mass of a regular soccer ball. How could the person kick the ball the same distance as the first soccer ball?

( will give brainliest if you help! )
( no trolling or I’ll report you)

Which of the following planets were the ancient Greeks able to see and make careful observations of?

Saturn and Neptune

Neptune and Uranus

Mars and Venus

Mercury and Uranus

If 11,550 J heat is absorbed by a copper object when it is heated from 20.0°C to 30.0°C,
what is the mass of the copper?
The specific heat of copper is 385 J/kgK.

Oberon is a moon of Uranus. It has a mass of 3.01 x 1021 kg and is 761.4 km away from Uranus. If the force of gravity
of Uranus is pulling 3.00 x 1025 N on Oberon, what is the mass of Uranus? (6 points)

PLEASE HELP!!!!
ITS URGENT!

write any three utilities of plastics​

Which are uses of convex mirrors? Check all that apply.

magnifying mirrors for putting on makeup
side-view mirrors on vehicles
hallway safety mirrors
focusing automobile headlights
lenses in sunglasses

On top labeled A 2 waves 1 above the other, with crests and troughs that line up. On bottom labeled B 2 waves, 1 above the other, so that the crests of the top wave line up with the troughs of the bottom wave.
Will there be noise cancellation in example A or example B?

PLEASE HELP What is it called when the moon passes through the penumbra of Earth’s shadow?(1 point)

total solar eclipse

partial solar eclipse

total lunar eclipse

partial lunar eclipse

If you could cut the paper in half 20 times, would the paper be bigger or smaller than the following: 1 hair--------------------, a germ-------------------- and an atom---------------------.

Do you think you could keep cutting the paper forever?-----------------------------------------

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Science

3. A bus is moving at 25 m/s when the driver steps on the brakes and brings the bus to a stop in 3.0 seconds. What is the average acceleration of the bus while braking?

A voltage is applied to a resistor,
which creates a 1.50 A current. If
you double the resistance, keeping
the voltage the same, what will the
new current be?
(Unit = A)

a mass of 0.8kg at the end of a rope 0.5m long is whirled round ina horizontal circle at an angular speed of 10 rads^-1. what is it's angular momentum?​

​A hose, of radius 0.018 m, is connected to a water faucet. The water pressure at the point where the hose connects to the faucet is 150,000 Pa. The other end of the hose is connected to an outlet of radius 0.011 m, where the water comes out. The total length of the hose and outlet is 15 m.
(a) An experiment shows that the water exists the outlet with a speed 5.2 m/s. What is the flow rate through the hose?
(b) What is the maximum height that the end of the outlet can he held above the faucet, and water still comes out?
(c) Suppose there is a small hole in the hose. How does that affect the speed at which the water comes out? Explain.

Explain each step!

PLEASE HELP ASAP
Q1. How would you record her BMI in an electronic medical record and would you include any notes?

Q2.What follow-up questions would be appropriate for the 15-year-old girl’s visit to the nutrition clinic, and why? What additional notes, if any, might be appropriate to enter into her electronic medical record, depending on her answers?

Q3.Based on everything you’ve read, which symptoms could indicate an eating disorder that might not be detectable by measuring BMI? What subjective and objective observations could you use to help detect other eating disorders in a clinical setting like the one described in this scenario?

Q4.Based on everything you’ve learned, explain which elements (symptoms, causes, contributing factors, etc.) of bulimia and/or anorexia are biological and physiological, and which are psychological, and which elements are sociological (based on an individual’s place in society, their relationship with other people, and the culture they live in). Include at least one element each for the physiological, psychological, and sociological elements.

Q5.Finally, engage in some independent research to examine BMI in more detail. Look up information that covers the following considerations:

- Limitations of the BMI scale, including considerations related to age, lifestyle, etc.

- How a BMI can be used as part of a “growth chart,” turning it from a one-time absolute measure of health into a dynamic measure of change over time

- How human’s nutrition needs change by age and lifestyle, e.g., do student athletes have different nutrition needs than average students? What about adult athletes?

Part Two i need one paragraph explaining this
The US Department of Agriculture has released an online tool, Choose My Plate, that aims to help people of all ages make healthy nutrition plans for themselves. Other countries have similar programs, so if you live outside the United States, you might see what your local recommendations are. Either way, remember these are just general guidelines, and ideally you would work directly with a physician or dietician to formulate a more individualized dietary plan.

Use the MyPlate Plan calculator on that site to find which calorie level is appropriate for you and follow its link to see your semi-personalized MyPlate plan. Based on the results, write a short paragraph explaining how closely you think your meals matched the proposed plan over the last three days. (If you want to make it even more relevant and you have the time, track everything you eat over the next three days and then write the paragraph. You might find that you get a more precise picture this way.) Are there areas for improvement, and if so, what steps might you take to achieve that improvement? Are there elements about your life that would make it difficult to keep to the proposed plan, like living in a food desert or not having healthy cafeteria options?

F = 480N

Mass = 15 kg

What is your acceleration?

A heat engine does 200 J of work per cycle while exhausting 400 J of waste heat. what is the engine's thermal efficiency?

A student lifts their 75 N backpack 0.50 m onto their chair. How much work is done?

[O.04H]The table below shows the use of some energy production methods over time.


Type of energy Average energy used annually in the past (in million tons) Average energy used annually at present (in million tons) Average energy most likely to be used annually in the future (in million tons)
Oil 200 4000 300
Gas 100 2500 700
Coal 1000 2500 1500
Wind 0.1 50 2000
Hydropower 0.7 60 150
Tidal power 0.02 50 500

Based on the table, which of these statements best describes the impact of different methods of energy production on the environment in the past?
There was a rise in the height of tides.
There was a rise in greenhouse gases.
The coastal ecosystem was harmed.
The coastal areas were highly polluted.

What is 6 °C in °F? round to one decimal place.

An electromagnetic wave moves through electric and magnetic fields. How might the movement of the wave be described?
A.
The vibrations of the fields are perpendicular to the direction in which the wave moves.
B.
The wave moves back and forth through the fields.
C.
The vibrations of the fields are parallel to the direction in which the wave moves.
close
D.
The wave moves through the fields in a random motion.

8) A force of 10 N stretches a spring 0.50 m from equilibrium. What is the value of the spring constant?​

The velocity of an object with mass = 2kg is given as a function of time:
V = 2ti + 4[tex]t^{2}[/tex]j

Find the force acting on the object at t = 2 seconds.

The cheetah is one of the fastest-accelerating animals, because it can go from rest to 27 m/s (about 60 mi/h) in 4.0 s. If its mass is 110 kg, determine the average power developed by the cheetah during the acceleration phase of its motion. Express your answer in

(a) watts

(b) horsepower.

A Body OF Volume 36cc Floats With 3/4 of its volume submerged in water . The density Of Body is

1. 0.25g/cc 2. 0.75g/cc
3. 0.9g/cc 4. 0.1g/cc​

A ball is thrown up at a 60 degree angle and lands in 18.5 seconds. what is the initial velocity of the ball?

Martin has hypothesized that the size and types of trees differ between valleys and higher elevations. He sets up a transect line in a wooded valley and randomly creates three 10 x 10 meter plots along the transect line, recording GPS coordinates for the northwest corner of each plot. He identifies and measures (diameter at breast height) every tree within the plots. He repeats this procedure in a wooded area on the ridge above the valley.

Using the scenario above, state the independent and dependent variables.

define prism and itz colo plz tell me fast​

In a 1953 experiment a rocket sled went from 284 m/s to rest within 178 m. If the test subject, John Stapp, had a mass of 84.0 kg: a) what is the amount of Work done to stop the John Stapp? b) how much Force was applied to John Stapp?