Particles connected with a string

In summary, the problem involves two particles connected by a string on a frictionless surface. When a small force is applied to the midpoint of the string, the particles move towards each other. The magnitude of acceleration when the separation between them is 2x is given by F/2mtanθ, which differs from the incorrect solution of F/2msinθ. The error lies in assuming the net force on each particle is T, when in fact it is a combination of T and the applied force.
  • #1
erisedk
374
7

Homework Statement



Two particle of mass m each are tied at the ends of a light string of length 2a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance ‘a’ from the center P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes 2x is
1422623933462Capture.PNG

Homework Equations

The Attempt at a Solution


http://2.bp.blogspot.com/_lRKubY9oOyI/RrGGAxqjRUI/AAAAAAAAAHQ/TtdYi47lpDc/s1600-h/Newton

2Tsinθ = F
T = F/2sinθ
where sinθ = (a2 - x2)1/2 / a
Net force on each particle is T.
So T = maacceleration
So, aacceleration = F/2msinθ

However, the answer is F/2mtanθ. I don't get why. Please help?
 
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  • #2
erisedk said:
Net force on each particle is T.
So T = maacceleration
So, aacceleration = F/2msinθ

Draw a free body diagram of the mass- do you get the net force on it to be T? you are making some serious error-the motion is along the plane towards the other body so net force can not be T.
 

Related to Particles connected with a string

1. What is a particle connected with a string?

A particle connected with a string is a physical system in which a small object, called a particle, is attached to a thin string or wire. The string acts as a constraint, limiting the movement of the particle to a specific trajectory.

2. What types of particles can be connected with a string?

Any small object with mass can be connected with a string, such as a ball, a pendulum, or even a small weight. The particle must be small enough for the string to support its weight and must be able to move in a constrained manner.

3. What is the purpose of connecting a particle with a string?

The string serves as a simple mechanism to study the motion and behavior of the particle. By connecting the particle with a string, we can control and manipulate its movement, making it easier to study and analyze.

4. How does the length of the string affect the particle's motion?

The length of the string determines the radius of the particle's trajectory. The longer the string, the larger the radius, and the slower the particle's motion. Conversely, a shorter string will result in a smaller radius and faster motion.

5. What are some real-life applications of particles connected with a string?

Particles connected with a string are commonly used in physics experiments and demonstrations, such as the famous "double pendulum" experiment. They can also be found in practical applications, such as in clocks and other timekeeping devices that use pendulums to regulate time.

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