At a point P, the electric field is 78 N/C at 51° counter-clockwise from the positive x axis. A particle of mass 4.7 kg and charge -0.11 C is located at P. Find:
1.the magnitude of the force on the particle
2.the direction of the force on the particle:
degrees counter-clockwise from the positive x axis
3. the magnitude of the acceleration of the particle: m/s2
4. the direction of the acceleration of the particle: degrees counter-clockwise from the positive x axis
I have tried F=qe
and Newton's second law F=ma
Let's start by solving each part of the problem step-by-step:
1. To find the magnitude of the force on the particle, we can use the formula F = qE, where F is the magnitude of the force, q is the charge of the particle, and E is the magnitude of the electric field. Plugging in the given values, we have:
F = (-0.11 C)(78 N/C) = -8.58 N
Therefore, the magnitude of the force on the particle is 8.58 N.
2. To find the direction of the force on the particle, we can use the given information that the electric field is at 51° counter-clockwise from the positive x-axis. Since the force and electric field are parallel, the force will have the same direction. Therefore, the direction of the force on the particle is 51° counter-clockwise from the positive x-axis.
3. To find the magnitude of the acceleration of the particle, we can use Newton's second law: F = ma, where F is the magnitude of the force and a is the magnitude of the acceleration. Rearranging the equation, we have:
a = F / m
Plugging in the given values, we get:
a = (-8.58 N) / (4.7 kg)
Calculating this, we find that the magnitude of the acceleration of the particle is approximately -1.8255 m/s^2.
4. To find the direction of the acceleration of the particle, we can use the information that the force on the particle is in the same direction as the electric field. Since the electric field is at 51° counter-clockwise from the positive x-axis, the acceleration will also be in the same direction. Therefore, the direction of the acceleration of the particle is 51° counter-clockwise from the positive x-axis.
To find the answers to the given questions, we will use the formulas related to electric fields and forces. Here's how you can solve each part:
1. Magnitude of the force on the particle:
The electric force on a particle is given by the equation F = qE, where F is the force, q is the charge of the particle, and E is the electric field. In this case, the charge of the particle is -0.11 C, and the electric field is 78 N/C. Substituting these values into the formula, we get:
F = (-0.11 C) * (78 N/C) = -8.58 N (since the charge is negative, the force will also be negative).
Therefore, the magnitude of the force on the particle is 8.58 N.
2. Direction of the force on the particle:
The direction of the force can be determined by the angle given in the question. It is given that the electric field is at an angle of 51° counter-clockwise from the positive x-axis. Since the force acting on the particle is in the same direction as the electric field, the direction of the force will also be 51° counter-clockwise from the positive x-axis.
3. Magnitude of the acceleration of the particle:
To find the magnitude of the acceleration, we need to use Newton's second law, which states that F = ma, where F is the force and a is the acceleration. We have already found the force acting on the particle in the first part as 8.58 N. The mass of the particle is given as 4.7 kg. Plugging these values into the formula, we get:
8.58 N = (4.7 kg) * a
Solving for a, we find:
a = 1.83 m/s²
Therefore, the magnitude of the acceleration of the particle is 1.83 m/s².
4. Direction of the acceleration of the particle:
Since the force and acceleration are in the same direction, and the force is 51° counter-clockwise from the positive x-axis as determined in part 2, the direction of the acceleration will also be 51° counter-clockwise from the positive x-axis.
So, the direction of the acceleration is 51° counter-clockwise from the positive x-axis.