Force analysis of a spring-bob system

In summary, the force analysis of a spring-bob system involves examining the forces acting on a mass attached to a spring, typically in a vertical or horizontal orientation. Key forces include gravitational force, spring force (according to Hooke's law), and any external forces applied to the system. The analysis helps in understanding the equilibrium position, oscillatory motion, and dynamics of the system, providing insights into parameters like spring constant, mass, and damping effects. This foundational concept is crucial for applications in physics and engineering involving oscillatory systems.
  • #1
tellmesomething
410
45
Homework Statement
A small bob of charge +Q and mass 5kg is suspended from a spring of force constant k=10^4N/m and is held at rest 50cm above an isolated point charge -Q fixed on the ground. The spring just stretched initially. When the bob is released, the naximun elongation of the spring is 10cm. Then Q=(25n)uc where n=?
Relevant Equations
None
I dont need anyone to do the sum directly please. I just need some hints, please dont give me the solution.

Im unable to understand how the bob will hit a maximum elongation, there are two forces accelerating the bob:
Gravitational force and electrostatic force.
There is one force deaccelerating it :
Spring Force

A max elongation means a point where the forces are balanced and the velocity of the bob equals 0

Would there be a point in time where the spring force becomes more than the downward force?

because I believe thats whats needed to make the velocity equal to 0 and then eventually the velocity vector would point in the upward direction
 
Physics news on Phys.org
  • #2
tellmesomething said:
Im unable to understand how the bob will hit a maximum elongation, there are two forces accelerating the bob:
Gravitational force and electrostatic force.
There is one force deaccelerating it :
Spring Force
Yes
tellmesomething said:
A max elongation means a point where the forces are balanced and the velocity of the bob equals 0
No. Think about the simple case of a ball thrown straight up in the air. At the highest point, v = 0. But, is the net force on the ball zero at this instant?

tellmesomething said:
Would there be a point in time where the spring force becomes more than the downward force?

because I believe thats whats needed to make the velocity equal to 0 and then eventually the velocity vector would point in the upward direction
Yes. That's right.

Hint: Energy rather than force is your friend here.
 
  • Like
Likes tellmesomething
  • #3
TSny said:
Yes

No. Think about the simple case of a ball thrown straight up in the air. At the highest point, v = 0. But, is the net force on the ball zero at this instant?


Yes. That's right.

Hint: Energy rather than force is your friend here.
Okay got it. Thankyou :-)
 
  • Like
Likes TSny

FAQ: Force analysis of a spring-bob system

What is a spring-bob system?

A spring-bob system consists of a mass (the bob) attached to a spring. When the mass is displaced from its equilibrium position, the spring exerts a restoring force that acts to return the mass to equilibrium. This system is often used to study oscillatory motion and the principles of Hooke's Law.

How does Hooke's Law apply to a spring-bob system?

Hooke's Law states that the force exerted by a spring is proportional to its displacement from the equilibrium position, expressed as F = -kx, where F is the restoring force, k is the spring constant, and x is the displacement. In a spring-bob system, this law helps to analyze the forces acting on the bob when it is displaced from its rest position.

What forces act on the bob in a spring-bob system?

The primary forces acting on the bob in a spring-bob system are the gravitational force (weight of the bob) and the spring force (restoring force). The net force acting on the bob determines its acceleration and motion according to Newton's second law of motion.

How can we analyze the motion of a spring-bob system?

The motion of a spring-bob system can be analyzed using differential equations derived from Newton's laws. By setting up the equation of motion, which incorporates the forces acting on the bob, we can solve for displacement, velocity, and acceleration over time, often leading to simple harmonic motion when the system is undamped.

What factors affect the oscillation frequency of a spring-bob system?

The oscillation frequency of a spring-bob system is influenced by the mass of the bob and the spring constant. The frequency of oscillation can be calculated using the formula f = (1/2π)√(k/m), where f is the frequency, k is the spring constant, and m is the mass of the bob. A stiffer spring (higher k) or a lighter bob (lower m) will result in a higher frequency of oscillation.

Similar threads

Calculating the spring force constant K
Replies
14
Views
1K
How can I determine the instant the block overcomes static friction?
2
Replies
61
Views
2K
Work: I am having problem determining the elongation in spring
Replies
10
Views
2K
Stretched spring attached to the center of a pure rolling disk
Replies
11
Views
555
Forces applied to a spring-loaded gas pedal
Replies
7
Views
754
Problem with when to use Force and Energy. What compresses spring/
Replies
3
Views
883
Energy Conservation as an explanation for v=0 for spring mass system
Replies
2
Views
943
Understanding the Forces Behind Part B of the Graph
Replies
10
Views
1K
What happens when the maximum is exceeded in the Mass-Spring System?
Replies
27
Views
3K
Two spring-coupled masses in an electric field (one of the masses is charged)
Replies
1
Views
472

Hot Threads

Recent Insights

Back
Top