In Fig. 12-41, a climber with a weight of 533.8 N is held by a belay rope connected to her climb

step 1 To the left is the free body diagram for the system. We are going to apply Newton's second law t

In Fig. 12-41, a climber with a weight of 533.8 N is held by...

In Fig. $12-41,$ a climber with a weight of 533.8 $\mathrm{N}$ is held by a belay rope connected to her climbing harness and belay device; the force of the rope on her has a line of action through her center of mass. The indicated angles are $\theta=40.0^{\circ}$ and $\phi=$ $30.0^{\circ} .$ If her feet are on the verge of sliding on the vertical wall, what is the coefficient of static friction between her climbing shoes and the wall?

In Fig. $12-41,$ a climber with a weight of 533.8 $\mathrm{N}$ is held by a
belay rope connected to her climbing
harness and belay device; the force of
the rope on her has a line of action through her center of mass. The indicated angles are $\theta=40.0^{\circ}$ and $\phi=$
$30.0^{\circ} .$ If her feet are on the verge of
sliding on the vertical wall, what is the coefficient of static friction between
her climbing shoes and the wall?

Key Concepts

Torque and Moment Equilibrium

Torque, or moment, refers to the rotational effect of a force about a pivot point. In equilibrium problems, not only must the linear forces balance, but the moments caused by these forces about any point must also sum to zero. This ensures that the object does not rotate, which is especially important when forces are applied at different angles and points on the body.

Force Decomposition

Force decomposition involves breaking vector forces into their horizontal and vertical components, or into components along other relevant axes. This technique is crucial in solving equilibrium problems because it allows the analysis of the influence of each component on the overall balance of forces.

Frictional Force and Coefficient of Static Friction

Friction is the resistive force that opposes motion between two contacting surfaces. The coefficient of static friction is a dimensionless value that quantifies the maximum frictional force available before sliding occurs, relative to the normal force. Determining this coefficient often involves comparing the forces that attempt to initiate movement with the available frictional resistance.

Static Equilibrium

In any problem involving objects at rest, static equilibrium requires that the sum of all forces and the sum of all moments (torques) acting on the object be zero. This principle allows one to set up equations that balance forces in each coordinate direction as well as torques about a chosen pivot point.

Free-Body Diagram

A free-body diagram is a graphical representation of all the forces acting on an object. It simplifies the analysis by isolating the object and showing forces such as weight, normal force, friction, and any applied forces with their directions, which is essential for correctly applying equilibrium conditions.

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