True or False: The northern & southern lights are caused by solar wind particles interacting with gases in our atmosphere.
1 answer:
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Answer:
Fe= 28.2 N : Magnitude of the equilibrant (Fe)
β = 18.34° , clockwise from the positive x axis
Explanation:
Concept of the equilibrant
It is called equilibrant to a force with the same magnitude and direction as the resulting one (in case it is non-zero) but in the opposite direction. Adding vectorially to all the forces (that is to say the resulting one) with the equilibrant you get zero
To solve this problem we decompose the forces given into x-y components to find the resulting force:
Look at the attached graphic
F₁= 33.4 N , θ₁=23.8° clockwise from the positive y axis (y+)
F₁x= 33.4 *sin23.8° = 13.48 N
F₁y= 33.4 *cos23.8° =30.6 N
F₂=46.1 N , θ₂=28.8 counterclockwise from the negative x axis (x-)
F₂x= -46.1 *cos28.8° = -40.4 N
F₂y= -46.1 *sin28.8° = -22.2 N
Components of the resultant in x-y R(x,y)
Rx= 13.48 N -40.4 N = - 26.92 N
Ry= 30.6 N -22.2 N = + 8.4 N
Components of the equilibrant in x-y Fe(x,y)
Fex= +26.92 N
Fey= - 8.4 N
Magnitude of the equilibrant (Fe)
Fe= 28.2 N
Angle the equilibrant makes with the x axis ( β)
β = -18.34°
β = 18.34° , clockwise from the positive x axis
Missing figure in the problem: https://www.physicsforums.com/attachments/p4-46-gif.117834/
Solution:
part a) The bucket is not moving so the resultant of the forces acting on it is zero. Let's apply the equation of equilibrium. We have:
so
where T=90.5 N is the tension of the rope, and a factor 2 is applied because the string holds the bucket twice. From this we find
part b) Here the situation is different: the string holds the bucket only in one point. Moreover, the bucket is pulled up at constant velocity, so zero acceleration: this means that the resultant of the forces acting on the bucket is zero. Therefore, the equation of equilibrium in this case is
and so, since we know from part a) that
, we can find the new tension T:
Solution:
part a) The bucket is not moving so the resultant of the forces acting on it is zero. Let's apply the equation of equilibrium. We have:
so
where T=90.5 N is the tension of the rope, and a factor 2 is applied because the string holds the bucket twice. From this we find
part b) Here the situation is different: the string holds the bucket only in one point. Moreover, the bucket is pulled up at constant velocity, so zero acceleration: this means that the resultant of the forces acting on the bucket is zero. Therefore, the equation of equilibrium in this case is
and so, since we know from part a) that