Draw the force vector starting at the black dot. The location, orientation, and length of the vector will be graded. You can mov
e the vectors F⃗ 1F→1 and F⃗ 2F→2 to construct the required vector, but be sure to return them into their initial positions before submitting the answer.
1 answer:
Answer:
F3 is the equilibrant force equal in magnitude to the resultant between F1 and F2 but opposite in direction to it.
Explanation:
Given the diagram, the force F3 to make the body remain at rest or in equilibrium is the equilibrant force, this force is equal in magnitude to the resultant Fr between F1 and F2 but opposite in direction to it.
See attachment for diagram of forces.
The resultant force;
Fr =√ (F1)² + (F2)²...(1) [diagram a]
Therefore the length of F3 is Fr
F3 = -Fr
The direction (diagram b) of the resultant force Fr is given by
∆ = acrtan[(F1/F2)]
The direction of F3 is [90 + arctan(F1/F2)]
As seen in the diagram (d), the location of the force is in the fourth quadrant.
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1)
The electrostatic force between two charges is given by
(1)
where
k is the Coulomb's constant
q1, q2 are the two charges
r is the separation between the charges
When the two spheres are brought in contact with each other, the charge equally redistribute among the two spheres, such that each sphere will have a charge of
where Q is the total charge between the two spheres.
So we can actually rewrite the force as
And since we know that
r = 1.41 m (distance between the spheres)
(the sign is positive since the charges repel each other)
We can solve the equation for Q:
So, the final charge on the sphere on the right is
2)
Now we know the total charge initially on the two spheres. Moreover, at the beginning we know that
(we put a negative sign since the force is attractive, which means that the charges have opposite signs)
r = 1.41 m is the separation between the charges
And also,
So we can rewrite eq.(1) as
Solving for q1,
Since , we can substituting all numbers into the equation:
which gives two solutions:
Which correspond to the values of the two charges. Therefore, the initial charge q1 on the first sphere is