Answer:
A. the magnitude of the force between the spheres is 3.97 x 10⁻⁴ N
B. the magnitude of its initial acceleration is 5.83 m/s²
Explanation:
given information:
metal sphere's mass, m = 0.1 g = 1 x 10⁻⁴ kg
charge, q = -21 nC = -2.1 x 10⁻⁸
r = 10 cm = 0.1 m
What is the magnitude of the force between the spheres?
F₁₂ = k q₁q₂/r²
= ( 9 x 10⁹) (-2.1 x 10⁻⁸)²/(0.1)²
= 3.97 x 10⁻⁴ N
If the upper sphere is released, it will begin to fall. What is the magnitude of its initial acceleration?
mg - F₁₂ = ma
a = g - (F₁₂/m)
= 9.8 - (3.97 x 10⁻⁴/1 x 10⁻⁴)
= 5.83 m/s²
Answer:
-15.708 rad/s^2
Explanation:
First, let us covert everything to the same unit. For me, I find dealing with radians/sec more intuitive, but you can solve it in rpm. We are told that the initial angular speed is 600 rpm and after 4 seconds it stops. Let's convert 600 rpm into radians/sec. To do this, multiply by 2*pi/60. This gives 62.83 rad/s. Now let's review our info:

Now we look up angular kinematics equations and the equation that has these parameters is

Substitute our values in:

Answer:

Explanation:
T = Tension on the string
E = Electric field
= Permittivity of free space = 
As the forces balance themselves we have the equations


Dividing the equations we get

Electric field is given by

The magnitude of the charge on each plate is 
Answer:
<em>The change of momentum of the dart is 0.84 Nw.s</em>
Explanation:
<u>Impulse and change of momentum</u>
The change in momentum of an object is its mass times the change in its velocity:

The change in the momentum can also be found by considering the force acting on it. If a force F acts for a time Δt, the change of momentum is given by:

The dart hits a dashboard with a net force of 14 N during the collision and stops in 0.06 seconds. The change of momentum is:

The change of momentum of the dart is 0.84 Nw.s