MHB Forces of 8N: Find Angle & Mass of Particle

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The discussion addresses the calculation of the angle between two forces of 8N that result in a 13N resultant. The angle is determined using the formula θ = π - arccos((2 * 8² - 13²) / (2 * 8²)), or alternatively θ = 2arccos(6.5 / 8). Additionally, it is established that the mass of the particle is 2kg, derived from the equation 7N = mg - 13N, leading to mg = 20N with g set at 10 m/s². The acute angle that one of the 8N forces makes with the surface is given by φ = (π - θ) / 2. The calculations and methodology are confirmed as correct.
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Two forces each of size 8N, have a resultant of 13N.

a) Find the angle between the forces

b) The two given forces of magnitude 8N act on a particle of mass m kg, which remains at rest on a horizontal surface with no friction. The normal contact force between the surface and the particle has magnitude 7N. Find m and the acute angle that one of the 8N forces makes with the surface.
 
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What have you done on this and where do you have a problem? Have you drawn the "force parallelogram" showing the addition of the forces?
 
Country Boy said:
What have you done on this and where do you have a problem? Have you drawn the "force parallelogram" showing the addition of the forces?
Hi , thanks I got the answer.
 
(a) angle between the two 8N forces is

$\theta = \pi - \arccos\left(\dfrac{2 \cdot 8^2 - 13^2}{2\cdot 8^2}\right)$, or $\theta = 2\arccos\left(\dfrac{6.5}{8}\right)$

(b) $7\,N = mg - 13\,N \implies mg = 20\,N \implies m = 2kg$ (using $g = 10 \, m/s^2$)

$\phi = \dfrac{\pi - \theta}{2}$
 
skeeter said:
(a) angle between the two 8N forces is

$\theta = \pi - \arccos\left(\dfrac{2 \cdot 8^2 - 13^2}{2\cdot 8^2}\right)$, or $\theta = 2\arccos\left(\dfrac{6.5}{8}\right)$

(b) $7\,N = mg - 13\,N \implies mg = 20\,N \implies m = 2kg$ (using $g = 10 \, m/s^2$)

$\phi = \dfrac{\pi - \theta}{2}$
Thank you so much!
 
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