Forces of 8N: Find Angle & Mass of Particle

• MHB
• Shah 72
In summary, the two given forces of size 8N have a resultant of 13N. To find the angle between the forces, one can use the equation $\theta = \pi - \arccos\left(\dfrac{2 \cdot 8^2 - 13^2}{2\cdot 8^2}\right)$ or $\theta = 2\arccos\left(\dfrac{6.5}{8}\right)$. Additionally, if the forces act on a particle with mass m on a horizontal surface with no friction and a normal contact force of 7N, the mass can be found using $7\,N = mg - 13\,N$ and the acute angle
Shah 72
MHB
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.

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!

1. What is the definition of a force?

A force is a push or pull that can cause an object to accelerate or change its motion.

2. How do you calculate the magnitude of a force?

The magnitude of a force can be calculated using the formula F=ma, where F is the force, m is the mass of the object, and a is the acceleration.

3. What is the relationship between force and acceleration?

According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

4. How do you find the angle of a force?

The angle of a force can be found using the formula tanθ = Fy/Fx, where θ is the angle, Fy is the vertical component of the force, and Fx is the horizontal component of the force.

5. How do you calculate the mass of a particle using the force and angle?

The mass of a particle can be calculated using the formula m = F/gsinθ, where m is the mass, F is the force, g is the acceleration due to gravity, and θ is the angle of the force.

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