An 800-N box is pushed up an inclined plane that is 4.0 m long. It requires 3200 J of work to

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An 800-N box is pushed up an inclined plane that is 4.0 m...

An $800-\mathrm{N}$ box is pushed up an inclined plane that is $4.0 \mathrm{~m}$ long. It requires $3200 \mathrm{~J}$ of work to get the box to the top of the plane, which is $2.0 \mathrm{~m}$ above the base. What is the magnitude of the average friction force on the box? (Assume the box starts at rest and ends at rest.) a) $0 \mathrm{~N}$ c) greater than $400 \mathrm{~N}$ b) not zero but d) $400 \mathrm{~N}$ less than $400 \mathrm{~N}$ e) $800 \mathrm{~N}$

An $800-\mathrm{N}$ box is pushed up an inclined plane that is $4.0 \mathrm{~m}$ long. It requires $3200 \mathrm{~J}$ of work to get the box to the top of the plane, which is $2.0 \mathrm{~m}$ above the base. What is the magnitude of the average friction force on the box? (Assume the box starts at rest and ends at rest.)
a) $0 \mathrm{~N}$
c) greater than $400 \mathrm{~N}$
b) not zero but
d) $400 \mathrm{~N}$
less than $400 \mathrm{~N}$ e) $800 \mathrm{~N}$

Key Concepts

Work-Energy Principle

The work-energy principle states that the net work done on an object is equal to its change in kinetic energy. In scenarios where an object starts and ends at rest, the total work done is fully expended in overcoming forces, such as friction and gravitational components, rather than changing the kinetic energy of the system.

Frictional Force

Frictional force is a resistive force that acts opposite to the direction of motion between two contacting surfaces. It converts some of the mechanical work into thermal energy, thereby reducing the efficiency of energy transfer in mechanical systems. Determining the magnitude of friction is crucial in solving problems where energy losses must be accounted for.

Inclined Plane

An inclined plane is a flat surface tilted at an angle, used to raise or lower objects by reducing the magnitude of the force required. This concept involves analyzing the components of gravitational force along the plane and highlights the interplay between applied force, gravitational pull, and friction in energy transformation processes.

Work

Work is the measure of energy transfer when a force acts upon an object to move it in the direction of the force. It is computed as the product of the force applied and the distance over which it acts. Understanding work is essential when analyzing energy changes in systems, such as objects being moved along surfaces.

Gravitational Potential Energy

Gravitational potential energy refers to the energy an object possesses due to its position in a gravitational field. When an object is elevated to a height, work must be done against gravity, which is stored as gravitational potential energy calculated by the product of the object's weight and its vertical displacement.

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