A sphere is charged with 2.5muC of charge. A second sphere is held 15 cm away has a charge of -4.5muC, and the magnitude of the force between them is 4.5 N. The first sphere has a mass of 500 g. In the absence of friction, how much will it accelerate with respect to the other sphere, in m/s^2?
First, we need to calculate the magnitude of the force between the two spheres using Coulomb's Law:
F = k * |q1 * q2| / r^2
where k = 9 x 10^9 N m^2/C^2 is the Coulomb constant, q1 = 2.5 x 10^-6 C is the charge of the first sphere, q2 = -4.5 x 10^-6 C is the charge of the second sphere, and r = 0.15 m is the distance between them.
Plugging in the values, we get:
F = (9 x 10^9) * |2.5 x 10^-6 * -4.5 x 10^-6| / (0.15)^2
F = 4.5 N
Now, we can use Newton's second law to find the acceleration of the first sphere:
F = m * a
where m = 0.5 kg is the mass of the first sphere and a is the acceleration we are trying to find.
Rearranging the equation, we get:
a = F / m
a = 4.5 / 0.5
a = 9 m/s^2
Therefore, the first sphere will accelerate at 9 m/s^2 with respect to the other sphere in the absence of friction.