A rigid, uniform, horizontal bar of mass m1 and length L is supported by two identical massless strings. (Figure 1) Both strings are vertical. String A is attached at a distance d
Rotational Equilibrium And Rotational Dynamics
In physics, the state of balance between the forces and the dynamics of motion is called the equilibrium state. The balance between various forces acting on a system in a rotational motion is called rotational equilibrium or rotational dynamics.
Equilibrium of Forces
The tension created on one body during push or pull is known as force.
A rigid, uniform, horizontal bar of mass m1 and length L is supported by two identical massless strings. (Figure 1) Both strings are vertical. String A is attached at a distance d<L/2 from the left end of the bar and is connected to the ceiling; string B is attached to the left end of the bar and is connected to the floor. A small block of mass m2 is supported against gravity by the bar at a distance x from the left end of the bar, as shown in the figure.
Throughout this problem positive torque is that which spins an object counterclockwise. Use g for the magnitude of the free-fall acceleration gravity.
Part A
Find TA, the tension in string A.
Express the tension in string A in terms of g, m1, L, d, m2, and x.
Part B
Find TB, the magnitude of the tension in string B.
Express the magnitude of the tension in string B in terms of TA, m1, m2, and g.
Part C
If the mass of the block is too large and the block is too close to the left end of the bar (near string B) then the horizontal bar may become unstable (i.e., the bar may no longer remain horizontal).
What is the smallest possible value of x such that the bar remains stable (call it xcritical)?
Express your answer for xcritical in terms of m1, m2, d, and L.
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