Moving in the x-direction, a particle carrying 1.0uC experiences no force. Moving with speed v at 30 degrees to the x-axis, the particle experiences a force of 2.0 N. What is the magnitude of the force it would experience if it moved along the y-axis with speed v?
http://physics.ucsd.edu/students/courses/summer2009/session1/physics2b/CH29.pdf
Problem 6
To find the magnitude of the force experienced by the particle if it moved along the y-axis with speed v, we can use trigonometry and the given information.
First, let's analyze the situation. We are told that when the particle moves in the x-direction, it experiences no force. This means that there is no component of force acting in the y-direction for that case.
When the particle moves with speed v at 30 degrees to the x-axis, it experiences a force of 2.0 N. This force is acting at an angle of 30 degrees with respect to the x-axis. We can break down this force into its x and y-components using trigonometry.
The x-component of the force (Fx) can be found using the equation:
Fx = Force * cos(angle)
Substituting the given value, we get:
Fx = 2.0 N * cos(30°)
Fx = 2.0 N * √3/2
Fx = √3 N
Since the particle is only moving along the y-axis, there is no component of force acting in the x-direction. Therefore, Fx = 0 N.
Now, let's find the y-component of the force (Fy). We can use the same equation as before:
Fy = Force * sin(angle)
Substituting the given value, we get:
Fy = 2.0 N * sin(30°)
Fy = 2.0 N * 1/2
Fy = 1.0 N
So, the magnitude of the force the particle would experience if it moved along the y-axis with speed v is 1.0 N.