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
Write the equation for centripetal force, and substitute the values T and L appropriately. Then with a bit of elementary algebra, rearrange the equation so that it solves for mass.
Express your answer in terms of the variables T, L, and v.
T=ma=mv²/L
m=TL/v²
The equation for centripetal force is given by the formula:
F = mv^2 / r
In this case, the force acting as centripetal force is the tension in the string denoted as T, and the radius of the circular motion is the length of the string denoted as L.
Substituting the values, we get:
T = m * v^2 / L
To solve for the mass, we can rearrange the equation in terms of m:
T * L = m * v^2
Dividing both sides of the equation by v^2, we get:
(T * L) / v^2 = m
So, the equation to solve for mass in terms of T, L, and v is:
m = (T * L) / v^2
To determine the equation for centripetal force, we can start with the definition of centripetal force: it is the net force acting toward the center of a circular path that keeps an object in uniform circular motion. For an object of mass m moving in a circular path of radius r at a speed v, this force can be represented as:
F_c = m * (v^2) / r
In this problem, the ice puck is attached to a horizontal string of length L and is revolving in a circle. The tension in the string provides the centripetal force to keep the puck in circular motion. So, T represents the centripetal force. We can equate these two forces:
T = m * (v^2) / L
Now, let's rearrange the equation to solve for the mass m. Multiply both sides of the equation by L, then divide it by (v^2):
m = (T * L) / (v^2)
Therefore, the equation to solve for the mass m is:
m = (T * L) / (v^2)
This equation expresses the mass in terms of the variables T, L, and v.