Final answer:
To analyze the motion of a puck being swung in a circle on a frictionless table, the key concepts are equilibrium, centripetal force, and the relationship between tension, mass, and acceleration due to gravity. The tension is the weight of the hanging mass, the radial force on the puck is the centripetal force, and the speed of the puck is determined by circular motion formulas. Changing the hanging mass will affect the puck's speed.
Step-by-step explanation:
The question relates to the concepts of centripetal force, tension in the string, and rotational motion in Physics. To describe the motion of a puck on a frictionless table which is tied to a string, with the string passing through a hole in the center of the table and an object of mass 2 hanging from the other end, we will use Newton's laws of motion, specifically focusing on circular motion dynamics.
(a) The tension in the string equals the weight of the hanging mass because it is in equilibrium. The formula for tension (T) then is T = mg, where m is the hanging mass and g is the acceleration due to gravity.
(b) The radial force acting on the puck is the centripetal force, which is provided by the tension in the string. It can be expressed as Fc = mrω2, where m is the mass of the puck, r is the radius of the circular path, and ω is the angular velocity.
(c) The speed of the puck (v) can be found using v = rω, where r is the radius and ω is the angular velocity of the puck.
(d) If mass 2 is increased, the tension in the string increases, which results in a higher centripetal force, causing the puck to move faster in its circular path.
(e) If mass 2 is decreased, the tension in the string decreases, leading to a lower centripetal force and, consequently, a slower speed of the puck in its circular motion.