Questions based on circular motion
An air puck of mass 0.034 kg is tied to a string and allowed to revolve in a circle of radius 1.2 m on a frictionless horizontal surface. The other end of the string passes through a hole in the center of the surface, and a mass of 1.7 kg is tied to it, as shown in the figure. The suspended mass remains in equilibrium while the puck revolves on the surface.
The acceleration of gravity is 9.81 m/s2 .
a) What is the magnitude of the force that maintains circular motion acting on the puck?
Answer in units of N.
b) What is the linear speed of the puck?
Answer in units of m/s.
According to the information provided we have one string that connects two objects. On one of the ends is a puck that is revolving on a horizontal, frictionless surface and on the other we have an object that is suspended freely.
The force with which the object that is suspended pulls the string providing the tension that acts as the centripetal force for the puck that is revolving. This force is equal to mass* acceleration due to gravity = 1.7*9.81 = 16.677 N.
Therefore the magnitude of the force that maintains circular motion acting on the puck is 16.677 N.
Now the tension in the string that maintains a circular motion in the puck is mv^2/r, where m is the mass of the puck, v is the linear velocity and r is the radius.
Therefore 16.677 = 0.034*v^2/ 1.2
=> v^2 = 16.677*1.2/0.034
=> v^2 = 588.6
=> v = 24.26 m/s.
The linear velocity of the puck is 24.26 m/s.