A worker pushed a 27 kg block 9.2 m along a level floor at constant speed with a force directe

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A worker pushed a 27 kg block 9.2 m along a level floor at...

A worker pushed a $27 \mathrm{~kg}$ block $9.2 \mathrm{~m}$ along a level floor at constant speed with a force directed $32^{\circ}$ below the horizontal. If the coefficient of kinetic friction between block and floor was $0.20$, what were (a) the work done by the worker's force and (b) the increase in thermal energy of the block-floor system?

A worker pushed a $27 \mathrm{~kg}$ block $9.2 \mathrm{~m}$ along a level floor at constant speed with a force directed $32^{\circ}$ below the horizontal. If the coefficient of kinetic friction between block and floor was $0.20$, what were
(a) the work done by the worker's force and (b) the increase in thermal energy of the block-floor system?

Key Concepts

Energy Conversion

Energy conversion in the context of friction involves transforming mechanical work into thermal energy. When an object moves at a constant speed under the influence of a force and friction, the work done by the applied force is balanced by the work done against friction, resulting in an increase in the thermal energy of the system.

Work

Work is the measure of energy transfer when a force causes a displacement. It is calculated as the dot product of the force and displacement vectors, which means only the component of the force in the direction of the movement contributes to the work. This is crucial when the force is applied at an angle, as only the horizontal component (if the displacement is horizontal) will do work on the object.

Force Decomposition

Force decomposition involves breaking a force into its horizontal and vertical components using trigonometric functions. This is essential in problems where the applied force is not aligned with the direction of motion, as the horizontal component contributes to displacement while the vertical component affects the normal force and, consequently, the frictional force.

Kinetic Friction

Kinetic friction is a resistive force that opposes the motion of objects sliding against each other. It is proportional to the normal force and the coefficient of kinetic friction. In problems with sliding motion at constant speed, the frictional force equals the component of the applied force opposing motion, and this frictional work is converted into thermal energy.

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