An object with mass m is attached to a string and the other end of the string is attached to a peg at the center of a level table. The object is set into uniform circular motion around the peg. The radius of the motion remains constant (the string does NOT wind up on the peg). The table and the peg are frictionless.
To analyze the scenario described, we can consider the forces acting on the object:
1. Tension Force (T): The string exerts tension on the object towards the center, providing the centripetal force required for circular motion.
2. Weight Force (W): The force due to gravity acting vertically downwards.
Since the object is in uniform circular motion, we know that the net force acting on it must be directed towards the center of the circular path. Therefore, the tension force in the string (T) must be equal in magnitude to the centripetal force required for circular motion.
The centripetal force (Fc) is given by the equation:
Fc = (mass x velocity^2) / radius
In this case, the velocity of the object is constant, and the radius remains constant, so the centripetal force is also constant.
Now, let's consider how to calculate the tension force (T):
1. Start by calculating the centripetal force (Fc) required for uniform circular motion using the given mass (m), velocity (v), and radius (r) of the motion.
2. Substitute the values into the equation: Fc = (m x v^2) / r
3. The magnitude of the tension force (T) is equal to the centripetal force (Fc).
Therefore, the tension force (T) can be calculated using the equation T = (m x v^2) / r.
Keep in mind that this analysis assumes ideal conditions, such as no friction or air resistance.