I need to determine maximum tension/down force with a pendulum.
I need to use the lightest string possible to:
-support a 16kg bob, with
-a velocity of 4m/s
-with a swing radius of 2m
-at it's equilibrium (ie 0 degrees)
-given standard gravity.
using T=m(V^2/r)+(g*cos(x))
The problem is as the swing radius (r) decreases then T increases.
But logic tells me it is opposite of this. What am I missing?
Thanks
also, any ideas of finding the exact gravitational force / gravitational acceleration data for my location?
no takers?
To determine the maximum tension/down force with a pendulum, let's break down the equation you provided: T = m(V^2/r) + (g*cos(x))
T represents the tension or downward force acting on the string. This force is a combination of the centripetal force (m(V^2/r)) and the gravitational force (m*g*cos(x)).
In this equation, m represents the mass of the bob, V is the velocity, r is the swing radius, g is the acceleration due to gravity, and x is the angle from the vertical (0 degrees in the case of equilibrium).
First, let's consider the right side of the equation. The centripetal force, m(V^2/r), is directly proportional to the mass of the bob and the square of its velocity, but inversely proportional to the swing radius. This means that as the swing radius decreases, the centripetal force increases.
Next, the gravitational force, m*g*cos(x), depends on the mass of the bob, the acceleration due to gravity, and the cosine of the angle from the vertical. In this case, at equilibrium (0 degrees), the cosine of 0 is 1, so the gravitational force is simply m*g.
So, the overall tension or downward force, T, is a combination of the centripetal force and the gravitational force. As the swing radius decreases, the centripetal force increases, but the gravitational force remains constant. Therefore, the tension or downward force also increases.
This may seem counterintuitive since we typically associate lighter strings with lower tensions. However, in the case of a pendulum, the swing radius plays a significant role in determining the tension. A smaller swing radius increases the magnitude of the centripetal force and requires a higher tension to maintain equilibrium.
To find the maximum tension/down force, you need to solve the equation for T using the given values of mass, velocity, swing radius, and angle.