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Monica [59]
4 years ago
9

Three children are struggling and pulling on a single toy. Two of the children, Abe and Barry, are EACH (individually) pulling w

ith 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):
Physics
1 answer:
3241004551 [841]4 years ago
8 0

Solution :

c). $\vec{F}_A = $ force applied by Abe

   $\vec{F}_B = $ force applied by Barry

   $\vec{F}_E = $ force applied by Eric

   $\vec{F}_R = $ Resultant force

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

         $\vec{F}_A = 0 \hat{i} + 60 \hat{j}$

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

         $\vec{F}_B = 60 \hat{i} + 0 \hat{j}$

The resultant,

$\vec{F}_R= \vec{F}_A+\vec{F}_B $

     $=(0 \hat i + 60 \hat j)+(60 \hat i + 0\hat j)$

    $=60 \hat i + 60 \hat j$

$|\vec{F}_R| = \sqrt{60^2+60^2}$

        = 84.853 N

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

$|\vec F_E| = |\vec F_R|$

$|\vec F_E| =84.853 \ N$

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 :

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

   $ = \tan ^{-1}\left(\frac{60}{60}\right)$

  = 45°  north east

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

   

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A billiard ball is moving in the x-direction at 30.0 cm/s and strikes another billiard ball moving in the y-direction at 40.0 cm
ipn [44]

To solve this problem it is necessary to apply the trigonometric ratios of the given velocity components.

If we make a graph of the velocity vectors in their respective velocities according to the given description we will have something similar to the attached graph.

The angle could be obtained from the components of the opposite leg and the adjacent leg so that

tan\theta = \frac{x}{y}

\theta = tan^{-1}(\frac{x}{y})

The opposite leg value (y) is 40cm / s and the adjacent leg (x) is 30cm / s

\theta = tan^{-1}(\frac{30}{40})

\theta = 36.87\°

Therefore the final direction that does the first ball is 36.87°

6 0
3 years ago
A 2cm length of wire centered on the origin carries a 20A current directed in the positive y direction. Determine the magnetic f
skad [1K]

Answer:

The magnetic field at a distance x = 5 m is 1.59 nT

Explanation:

Length of the wire, L = 2 cm = 0.02 m

Current, I = 20 A

x = 5 m

Magnetic field at a distance x = 5 m due to an infinitely long wire is given by:

B = \frac{\mu_{o}IL}{4\pi x\sqrt{x^{2} + L^{2}}}

B = \frac{4\pi\times 10^{- 7}\times 20\times 0.02}{4\pi \times 5\sqrt{5^{2} + 0.02^{2}}} = 1.59\times 10^{- 9}\ T

3 0
3 years ago
1. Suppose you're working at a constant temperature , when you exert more pressure on an object
vova2212 [387]

Answer:

Decrease

Explanation:

Working at a constant temperature when more pressure is exerted, the volume decreases.

This is known as Boyle's law.

 According to Boyle's law;

       "the volume of a fixed mass of a gas varies inversely as the pressure changes, if the temperature is constant".

  Mathematically;

          P₁V₁  = P₂V₂

P and V are pressure and volume

1 and 2 are initial and final states.

8 0
3 years ago
What’s the answer to this question
alexgriva [62]

Answer:

space = 66.24 [m]

Explanation:

To solve this problem we must remember that the average speed is defined as the relationship between a space traveled over a certain time.

Av = \frac{space}{time}

where:

space [m]

Av = average velocity = 3.6 [m/s]

time = 18.4 [s]

space = 3.6*18.4\\space = 66.24 [m]

7 0
3 years ago
Please help on this one?
valina [46]

I believe that it is d correct me if wrong because the higher the temperature the more active the molecules are gonna be, but the graph does not explicitly state that, so you can say the answer is d (if not the answer is c) (sorry if wrong)

3 0
3 years ago
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