A solid uniform 45.0-kg ball of diameter 32.0 cm is supported against a vertical frictionless wa

step 1 Question number 13, this is the vertical wall and a sphere is attached to it by a string. The le

A solid uniform 45.0-kg ball of diameter 32.0 cm is...

A solid uniform $45.0-\mathrm{kg}$ ball of diameter 32.0 $\mathrm{cm}$ is supported against a vertical frictionless wall using a thin $30.0-\mathrm{cm}$ wire of negligible mass, as shown in Fig. 5.47. (a) Make a free-body diagram for the ball and use it to find the tension in the wire. (b) How hard does the ball push against the wall? figure can't copy

Key Concepts

Static Equilibrium

Static equilibrium is the condition in which all forces and torques acting on an object cancel out, so the object remains at rest with no linear or angular acceleration. This concept is fundamental in analyzing systems where forces such as gravity, tension, and normal forces interact, ensuring that the sum of all forces and the sum of all moments (torques) equal zero.

Free-Body Diagram

A free-body diagram is a schematic that isolates an object to show all external forces acting upon it, including their directions and points of application. This tool is essential for setting up the equations necessary to solve for unknown forces in problems involving static or dynamic equilibrium.

Torque (Moment) Balance

Torque, or moment of force, is the rotational influence exerted by a force applied at a distance from a pivot point. In equilibrium, the sum of the torques about any axis must be zero. This principle allows one to relate different forces acting at various lever arms and is critical in solving for tensions or reaction forces in systems involving rotational balances.

Force Components Analysis

Analyzing forces by breaking them into their horizontal and vertical components simplifies the process of applying equilibrium conditions. This method allows the separate consideration of forces in different directions, making it easier to set up and solve the equations for the balance of forces, especially when forces are applied at angles.

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