Physics, 08.02.2021 19:20 dsanders20

While sliding a couch across a floor, Hannah and Andrea exerts forces FH and FA on the couch. Hannah's force is due north with a magnitude of FH = 59 N and Andrea's force is θ = 22° east of north with a magnitude of FA = 155 N. In this problem, use a coordinate system with y directed north and x directed east. Part (a) Find the net force in the y-direction in Newtons.
Part (b) Find the net force in the x-direction in Newtons.
Part (c) Calculate the angle in degrees north of east of the net force exerted on the couch by Hannah and Andrea, F HAF→HA.
Part (d) Hannah and Andrea's housemates, David and Stephanie disagree with the move and want to prevent its relocation. Their combined force F DSF→DS must be equal and opposite to that of FHAF→HA. What is the magnitude in Newtons of the force F DSF→DS which will prevent the relocation?

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Answer from: shawntawright1

a) 202.7 N

b) 58.1 N

c) 74.1º N of E.

d) 210.9 N

Explanation:

The net force exerted in the y-direction, will be the sum of FH (which is directed northwards) and the y-component of FA.Since the magnitude of FA is 155 N and the angle of FA with the y-axis, is 22º (E of N), we can find the N-S component of FA, just applying the the definition of cosine, to the triangle defined by FA, the y- axis and a segment parallel to the x- axis between FA and the y-axis, as follows:

$F_{Ay} = F_{A} * cos \theta = 155 N* cos 22 = 143.7 N (1)$

⇒ Fy = FH + FAy = 59 N + 143.7 N = 202.7 N (2)

We can proceed exactly in the same way for the x-axis. Since FH is directed due North, it has no component along the x-axis.So, Fx is directly the component of FA along the x-axis, which can be found applying the definition of sine to the same triangle than in a) as follows:

$F_{x} = F_{A} * sin \theta = 155 N* sin 22 = 58.1 N (3)$

Taking the same triangle than in a) and b), we can apply the definition of tangent, in order to find the angle between F and the x-axis, as follows:

$tg \theta = \frac{F_{y}}{F_{x}} = \frac{202.7N}{58.1N} = 3.5 (4)$

⇒ θ = tg⁻¹ (3.5) = 74.1º N of E. (5)

In order to be equal and opposite to the combined force FH+FA, it must have the same magnitude.This magnitude can be found applying the Pythagorean Theorem to the same triangle that we used in a), b) and c):

$F_{DS} = \sqrt{(F_{x} ^{2} +F_{y} ^{2})} = \sqrt{(58.1N)^{2}) + (202.7N)^{2} } = 210.9 N (6)$

Answer from: Quest

answer: the rock sample is a sedimentary rock.

explanation:

it is given that:

mass of rock sample, m = 2.7 g

volume of rock sample, $v = 1.1 cm^{3}$

so, density of rock sample will be

$density = \frac{mass}{volume}$

$\rho =\frac{2.7}{1.1}g/cm^{3}\\\\\rho =2.45 g/cm^{3}$

since, the density of rock sample is $2.45 g/cm^{3}$ . hence, the rock sample is a sedimentary rock, whose densities varies between $2g/cm^{3} - 2.6 g/cm^{3}$ .

Answer from: Quest

the skeletons of most mammals reach a certain size and then stop growing. however, many animals, including some mammals, keep growing throughout their lives. kangaroos, for example, just keep growing and growing until they die. also, the longer an animal lives the greater the chance it might catch some deadly disease.

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