To find the electric force exerted on the sphere, we need to consider the forces acting on it: the force due to gravity and the force due to the compressed spring.
1. Force due to gravity: The weight of the sphere can be calculated using the formula:
F_gravity = mass × acceleration due to gravity
F_gravity = 1.20 kg × 9.8 m/s^2
F_gravity = 11.76 N
This force acts downward.
2. Force due to the compressed spring: The force exerted by a spring can be calculated using Hooke's law:
F_spring = -k × Δx
where k is the spring constant and Δx is the change in length of the spring.
Δx = Final length - Relaxed length
= 0.0950 m - 0.100 m
= -0.005 m
Note: The negative sign indicates that the spring is compressed.
F_spring = -450 N/m × (-0.005 m)
= 2.25 N
This force acts upward.
Now, let's consider the net force acting on the sphere:
Net force = F_spring + F_gravity
= 2.25 N + 11.76 N
= 14.01 N
The magnitude of the electric force exerted on the sphere is 14.01 N.
Since the net force is directed upward, the direction of the electric force exerted on the sphere is also upward.
A plastic spring with spring constant 450 N/m has a relaxed length of 0.100 m. The spring is positioned vertically on a table, and a charged plastic 1.20-kg sphere is placed on the top end of the spring. Another charged object is suspended above the sphere without making contact. If the length of the spring is now 0.0950 m, what are the magnitude and direction of the electric force exerted on the sphere?
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