A window washer pushes his scrub brush up a vertical window...

A window washer pushes his scrub brush up a vertical window at constant speed by applying a force $\vec{F}$ as shown in Fig. 5.65 . The brush weighs 12.0 $\mathrm{N}$ and the coefficient of kinetic friction is $\mu_{k}=0.150 .$ Calculate $(a)$ the magnitude of the force $\frac{(a)}{\vec{F}}$ and (b) the normal force exerted by the window on the brush.

A window washer pushes his scrub brush up a vertical window at constant speed by applying
a force $\vec{F}$ as shown in Fig. 5.65 . The brush weighs 12.0 $\mathrm{N}$ and the coefficient of kinetic friction is $\mu_{k}=0.150 .$ Calculate $(a)$ the magnitude of the force $\frac{(a)}{\vec{F}}$ and
(b) the normal force exerted by the window on the brush.

Key Concepts

Normal Force

The normal force is the perpendicular contact force exerted by a surface on an object. It plays a critical role in frictional problems because it directly affects the magnitude of frictional forces acting on the object. Understanding how changes in other applied forces can alter the normal force is important for correctly analyzing and solving these situations.

Force Decomposition

Force decomposition involves breaking a force vector into its horizontal and vertical components using trigonometric functions. In problems where forces are applied at an angle, decomposing the forces allows for the separate analysis of effects in each dimension, which is essential for applying equilibrium conditions and solving for unknown quantities.

Newton's Laws and Equilibrium

This concept refers to the idea that when an object moves at constant velocity, its acceleration is zero, meaning the net force acting on it is zero. In problems like this, all forces acting on the object, including gravity, friction, and the applied force, must balance each other out, which provides a basis for setting up equations to solve for unknown forces.

Kinetic Friction

Kinetic friction is the resistive force that opposes the motion of an object sliding over a surface. It is calculated as the product of the kinetic friction coefficient and the normal force. This concept is crucial when analyzing systems where movement is involved, as it directly influences the net force required to maintain motion at a constant speed.

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