A vaulter holds a 29.4 N pole in equilibrium by exerting an...

A vaulter holds a 29.4 $\mathrm{N}$ pole in equilibrium by exerting an upward force $\overrightarrow{\mathrm{U}}$ with her leading hand and a downward force $\overrightarrow{\mathbf{D}}$ with her trailing hand as shown in Figure $\mathrm{P} 12.21 .$ Point $C$ is the center of gravity of the pole. What are the magnitudes of $\overrightarrow{\mathbf{U}}$ and $\overrightarrow{\mathbf{D}}$ ? GRAPH CANNOT COPY

Key Concepts

Static Equilibrium

Static equilibrium is the condition in which an object remains at rest because the net force and net torque acting on it are zero. In this context, the vaulter’s actions create forces that balance both the weight of the pole and the moments (torques) about its center of gravity, ensuring that the pole does not move or rotate.

Force Equilibrium

Force equilibrium involves ensuring that the vector sum of all forces acting on a body is zero. For the pole, this means that the upward and downward forces applied by the vaulter must add up to counteract the gravitational force, which keeps the object stationary in the vertical direction.

Torque Equilibrium

Torque equilibrium is achieved when the sum of the moments (torques) about any pivot point is zero. For an object in equilibrium, the torques produced by forces applied at different points must cancel each other out. This principle is critical in determining the magnitudes of the forces applied by the vaulter in different directions about the pole’s center of mass.

Center of Gravity

The center of gravity of an object is the average location of its weight distribution, and it is the point where gravity can be considered to act. When analyzing equilibrium, particularly torque balance, it is important to consider the moments created about the center of gravity to ensure accurate calculations of force magnitudes.

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