An ice puck of mass m revolves on an icy surface in a circle at speed v at the end of a horizontal string of length L. The tension in the string is T
Find the mass of the puck when the length of the string is 2.2m , string tension is 5.0N , and the tangential speed of the puck is 3.0m/s .
Express your answer to two significant figures and include the appropriate units.
To find the mass of the puck, we can use the centripetal force equation:
T = (m * v^2) / r
Where T is the tension in the string, m is the mass of the puck, v is the tangential speed of the puck, and r is the radius of the circular path.
In this case, we are given the length of the string L, which is the radius of the circular path. So we have r = L = 2.2m.
We are also given the tension in the string T = 5.0N and the tangential speed v = 3.0m/s.
Plugging these values into the centripetal force equation, we have:
5.0N = (m * (3.0m/s)^2) / (2.2m)
Simplifying the equation:
5.0N * 2.2m = m * (3.0m/s)^2
11.0N*m = 9.0m^3/s^2
Dividing both sides of the equation by (9.0m^3/s^2), we get:
m = (11.0N*m) / (9.0m^3/s^2)
m ≈ 1.22 kg (rounded to two significant figures)
Therefore, the mass of the puck is approximately 1.22 kg.