A 520-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 110-N rod as indicated in the figure below. The left end of the rod is supported by a hinge and the right end is supported by a thin cable making a 30.0° angle with the vertical. (Assume the cable is connected to the very end of the 6.00-m-long rod, and that there are 2.00 m separating the wall from the sign.) A rectangular sign hangs along the bottom of a rod connected to a hinge on a wall on its left. A cable with tension T at the right end of the rod connects to the wall above the hinge and makes a 30.0° angle with the vertical. The right end of the sign is at the right end of the rod. (a) Find the (magnitude of the) tension T in the cable. N (b) Find the horizontal and vertical components of the force exerted on the left end of the rod by the hinge. (Take up and to the right to be the positive directions. Indicate the direction with the sign of your answer.)
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 520-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 110-N rod as indicated in the figure below. The left end of the rod is supported by a hinge and the right end is supported by a thin cable making a 30.0° angle with the vertical. (Assume the cable is connected to the very end of the 6.00-m-long rod, and that there are 2.00 m separating the wall from the sign.)
A rectangular sign hangs along the bottom of a rod connected to a hinge on a wall on its left. A cable with tension T at the right end of the rod connects to the wall above the hinge and makes a 30.0° angle with the vertical. The right end of the sign is at the right end of the rod.
(a) Find the (magnitude of the) tension T in the cable.
N
(b) Find the horizontal and vertical components of the force exerted on the left end of the rod by the hinge. (Take up and to the right to be the positive directions. Indicate the direction with the sign of your answer.)
![### Problem Description
A 520-N uniform rectangular sign, measuring 4.00 m wide and 3.00 m high, is suspended from a horizontal, 6.00-m-long, uniform, 110-N rod as indicated in the figure below. The left end of the rod is supported by a hinge and the right end is supported by a thin cable making a 30.0° angle with the vertical. Assume the cable is connected to the very end of the 6.00-m-long rod, and that there are 2.00 m separating the wall from the sign.
### Diagram Description
The diagram shows a rectangular sign that reads "ICE CREAM SHOP" hanging from the right end of a horizontal rod. The rod is hinged on its left end and the right end is supported by a cable. The cable makes a 30.0° angle with the vertical.
### Part (a)
**Problem Statement:**
Find the (magnitude of the) tension \( T \) in the cable.
\[
\boxed{\hspace{2cm}} \, \text{N}
\]
### Part (b)
**Problem Statement:**
Find the horizontal and vertical components of the force exerted on the left end of the rod by the hinge. (Take up and to the right to be the positive directions. Indicate the direction with the sign of your answer.)
\[
\begin{aligned}
\text{horizontal component} & \quad \boxed{\hspace{2cm}} \, \text{N} \\
\text{vertical component} & \quad \boxed{\hspace{2cm}} \, \text{N} \\
\end{aligned}
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