In Figure 9.20, the cg of the pole held by the pole vaulter is 2.00 m from the left hand, and t

step 1 A simplified diagram for this problem is the weight acts from the center, 2 meter away, F2 acts,

In Figure 9.20, the cg of the pole held by the pole vaulter...

In Figure 9.20, the $\mathrm{cg}$ of the pole held by the pole vaulter is $2.00 \mathrm{~m}$ from the left hand, and the hands are $0.700 \mathrm{~m}$ apart. Calculate the force exerted by (a) his right hand and (b) his left hand. (c) If each hand supports half the weight of the pole in Figure 9.18, show that the second condition for equilibrium (net $\tau=0$ ) is satisfied for a pivot other than the one located at the center of gravity of the pole. Explicitly show how you follow the steps in the Problem-Solving Strategy for static equilibrium described above.

Key Concepts

Force Distribution in Lever Systems

In lever systems, forces are often distributed unevenly along the length of the lever. Analyzing how these forces contribute to both translational and rotational equilibrium involves understanding the balance of forces and torques. This concept is applied in scenarios where different points of application (such as hands on a pole) support varying amounts of load, and it is essential for ensuring the system remains in equilibrium.

Center of Gravity

The center of gravity of an object is the point where the total weight of the body is thought to be concentrated. In statics problems, assuming that the weight acts at the center of gravity simplifies the process of analyzing rotational equilibrium. This concept is especially important in problems where the distribution of weight affects the balance and torque calculations.

Lever Arm

A lever arm is the perpendicular distance from the pivot point to the line of action of the force. The concept of the lever arm is crucial in calculating torque, as even a small force can produce a large torque if applied at a large distance from the pivot. This principle is used to analyze how forces applied at different distances contribute to the overall equilibrium of a system.

Static Equilibrium

In statics, a system is in equilibrium when both the net force and the net torque acting on it are zero. This means that all the forces balance out so there's no linear acceleration and all the torques balance so there is no rotational acceleration. This concept is the foundation for analyzing and solving problems where objects are at rest or moving at constant velocity.

Torque

Torque, also known as moment of force, quantifies the tendency of a force to cause rotation about a pivot or axis. It is calculated by multiplying the force by the perpendicular distance from the pivot to the line of action of the force. Understanding torque is essential for solving equilibrium problems because it helps determine how forces applied at different points affect rotational balance.

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