a small sphere with a mass of 108.0 g is moving along the y-axis when it encounters an electric field of 5.0i N/C . If the sphere suddenly accelerates
13.0i m/s^2, what is the charge that it carries?
Please explain
To find the charge that the sphere carries, we can use the equation that relates the force experienced by an object in an electric field to its charge:
F = qE
Where:
F is the force experienced by the object,
q is the charge of the object,
E is the electric field.
In this case, the electric field is given as 5.0i N/C where i represents the unit vector in the positive x-direction. The force experienced by the sphere can be determined using Newton's second law:
F = ma
Where:
m is the mass of the sphere,
a is the acceleration experienced by the sphere.
The mass of the sphere is given as 108.0 g, which is equivalent to 0.108 kg. The acceleration is given as 13.0i m/s^2. Therefore, the force experienced by the sphere can be calculated as:
F = (0.108 kg)(13.0i m/s^2)
= 1.404i N
Now, we can equate this force to the product of the charge and the electric field:
1.404i N = q(5.0i N/C)
To find the charge, we need to isolate q. Since both sides of the equation have the i component, we can remove it to obtain the scalar equation:
1.404 N = 5.0q C
Finally, dividing both sides of the equation by 5.0 C gives us the value of q:
q = 1.404 N / 5.0 C
= 0.2808 C
Therefore, the charge that the sphere carries is 0.2808 coulombs.