Answer :
The mechanism uses the spring force to propel the small sphere along the circular track. The tension in the string provides the centripetal force required to keep the sphere in circular motion. The speed of the sphere varies along the track, being highest at the bottom and lowest at the top.
The mechanism shown in the figure is used to project a small sphere around a circular track with a radius of R = 1.5m. When s = 0, the spring in the firing mechanism is unstretched.
To understand how the mechanism works, let's break it down step by step:
1. The mechanism consists of a spring-loaded launcher and a circular track. The spring in the launcher is initially unstretched when s = 0.
2. When the spring is released, it exerts a force on the small sphere, propelling it forward. This force is known as the spring force and is given by Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.
3. As the small sphere moves along the circular track, it experiences a centripetal force that keeps it in a circular motion. This force is directed towards the center of the circular track and is given by the equation Fc = mv²/r, where Fc is the centripetal force, m is the mass of the sphere, v is its velocity, and r is the radius of the circular track.
4. The centripetal force is provided by the tension in the string attached to the sphere. The tension force is directed towards the center of the circle and acts as the centripetal force, allowing the sphere to maintain circular motion.
5. As the sphere moves along the circular track, its speed changes. At the bottom of the track, where the radius is maximum, the speed of the sphere is highest. At the top of the track, where the radius is minimum, the speed is lowest. This is because the centripetal force required to keep the sphere in circular motion is highest at the bottom and lowest at the top.
6. The sphere continues to move along the circular track until it completes one full revolution or until it loses enough energy due to friction or air resistance to come to a stop.
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