All categories

3 years ago

Determine the magnitude and direction of the resultant force of the following free body diagram.

Physics

1 answer:

Papessa [141]3 years ago

4 0

Answer:

The magnitude and direction of the resultant force are approximately 599.923 newtons and 36.405°.

Explanation:

First, we must calculate the resultant force ( $\vec F$ ), in newtons, by vectorial sum:

$\vec F = [(-200\,N)\cdot \cos 60^{\circ}+(400\,N)\cdot \cos 45^{\circ}+300\,N]\,\hat{i} + [(200\,N)\cdot \sin 60^{\circ} + (400\,N)\cdot \sin 45^{\circ}-100\,N]\,\hat{j}$ (1)

$\vec F = 182.843\,\hat{i} + 356.048\,\hat{j}$

Second, we calculate the magnitude of the resultant force by Pythagorean Theorem:

$\|\vec F\| = \sqrt{(482.843\,N)^{2}+(356.048\,N)^{2}}$

$\|\vec F\| \approx 599.923\,N$

Let suppose that direction of the resultant force is an standard angle. According to (1), the resultant force is set in the first quadrant:

$\theta = \tan^{-1}\left(\frac{356.048\,N}{482.843\,N} \right)$

Where $\theta$ is the direction of the resultant force, in sexagesimal degrees.

$\theta \approx 36.405^{\circ}$

The magnitude and direction of the resultant force are approximately 599.923 newtons and 36.405°.

You might be interested in

How can you make the potential energy as high as possible in a magnetic field between one electromagnet and one piece of iron?

harkovskaia [24]

In step 1, to increase the potential energy, the iron will move towards the electromagnet.

In step 2, to increase the potential energy, the iron will move towards the electromagnet.

<h3>Potential energy of a system of magnetic dipole</h3>

The potential energy of a system of dipole depends on the orientation of the dipole in the magnetic field.

$U = \mu B$

where;

$\mu$ is the dipole moment
B is the magnetic field

$B = \frac{\mu_0 I}{2\pi r}$

$U = \mu\times (\frac{\mu_0 I}{2\pi r} )$

Increase in the distance (r) reduces the potential energy. Thus, we can conclude the following;

In step 1, to increase the potential energy, the iron will move towards the electromagnet.
In step 2, when the iron is rotated 180, it will still maintain the original position, to increase the potential energy, the iron will move towards the electromagnet.

Learn more about potential energy in magnetic field here: brainly.com/question/14383738

7 0

2 years ago

An uniform electric field of magnitude E = 100 N/C is oriented along the positive y-axis. What is the magnitude of the flux of t

Ede4ka [16]

Answer:

The magnitude of the flux of electric field through a square of surface area is zero.

Explanation:

$E=100 NC^{-1}\\\\A=2 m^2\\\\Electic\,\,flux\,\,flux\,\,is\,\,given\,\,as:\\\\\phi_E=E.A\,cos\,\theta$

It is given that square box is parallel to yz-plane which has normal vector perpendicular to plane in x-direction. Angle between normal vector of area and electric field is 90°. Substituting in (1)

$\phi_E=E.A\,cos\,(90^o)\\\\\phi_E=0$