The figure shows four electrical charges located at the corners of a rectangle. Like charges, you will recall, repel each other while opposite charges attract. Charge B exerts a repulsive force (directly away from B) on charge A of 3.0 . Charge C exerts an attractive force (directly toward C) on charge A of 6.0 . Finally, charge D exerts an attractive force of 2.0 on charge A.

141cm
Figure: A--------B
100cm | |
| |
C--------D

(1) Assuming that forces are vectors, what is the magnitude of the net force exerted on charge A?
(2) What is the direction of the net force exerted on charge A? (degrees counterclockwise to the left)

On A

to the left, 3,
downward, 6
the diagonal can be then
downward (2*costheta=2*1/sqrt5)
and to the right 2 sinTheta=2*sqrt2/sqrt5

check those, the trig functions are a result of the dimensions.

Finally, add the downward and horizontal as vectors.

To answer these questions, we need to calculate the net force exerted on charge A by charges B, C, and D. We will use vector addition to find the magnitude and direction of the net force.

(1) To find the magnitude of the net force, we need to calculate the sum of the forces in the x and y directions. Assuming the positive x-axis is to the right and the positive y-axis is upward:

The force exerted by charge B on charge A is 3.0 (directly away), which means it only has a component in the x-direction.
The force exerted by charge C on charge A is 6.0 (directly toward), which means it has components in both the x and y directions.
The force exerted by charge D on charge A is 2.0 (directly toward), which means it has components in both the x and y directions.

To calculate the net force in the x-direction, we need to subtract the force exerted by charge B from the x-component of the force exerted by charge C, and add the x-component of the force exerted by charge D.

Net force in the x-direction = Fx(C) - Fx(B) + Fx(D)

Next, we calculate the net force in the y-direction by adding the y-components of the forces exerted by charges C and D.

Net force in the y-direction = Fy(C) + Fy(D)

Finally, we use the Pythagorean theorem to find the magnitude (net force) of the vector sum of the forces in the x and y directions:

Magnitude of the net force = √[ (Net force in the x-direction)^2 + (Net force in the y-direction)^2 ]

(2) To find the direction of the net force exerted on charge A (counterclockwise to the left), we can use trigonometry to calculate the angle between the net force vector and the positive x-axis.

Angle (direction) = atan2(Net force in the y-direction, Net force in the x-direction)

Now, let's plug in the given values and calculate the answers.

(Note: The distance between charges is not used in these calculations; it is only provided for reference in the figure).

Answer:
(1) Magnitude of the net force exerted on charge A: Calculate the net force in the x and y directions, and then use the Pythagorean theorem to find the magnitude of the vector sum.

(2) Direction of the net force exerted on charge A (degrees counterclockwise to the left): Use trigonometry to calculate the angle between the net force vector and the positive x-axis.

To determine the magnitude of the net force exerted on charge A, we need to consider the vector sum of the individual forces.

(1) Using Pythagoras' theorem, we can find the total force in the x-direction:
Fx = -3.0 + 2.0 = -1.0 N

The total force in the y-direction is:
Fy = 6.0 N

To find the net force magnitude, we can use the Pythagorean theorem:
|Fnet| = √(Fx^2 + Fy^2)
|Fnet| = √((-1.0)^2 + 6.0^2)
|Fnet| = √(1.0 + 36.0)
|Fnet| = √37
|Fnet| ≈ 6.082 N

Therefore, the magnitude of the net force exerted on charge A is approximately 6.082 N.

(2) To determine the direction of the net force, we can find the angle using trigonometry:
θ = arctan(Fy / Fx)
θ = arctan(6.0 / -1.0)
θ ≈ -80.54°

The negative sign indicates an angle in the clockwise direction. However, since we're looking for the angle counterclockwise to the left, we need to add 180° to obtain the correct direction:
θ = -80.54° + 180°
θ ≈ 99.46°

Therefore, the direction of the net force exerted on charge A is approximately 99.46° counterclockwise to the left.