Monica pulls her daughter Jessie in a bike trailer. The...

Monica pulls her daughter Jessie in a bike trailer. The trailer and Jessie together have a mass of 25 kg. Monica starts up a $100-\mathrm{m}-\mathrm{long}$ slope that's $4.0 \mathrm{m}$ high. On the slope, Monica's bike pulls on the trailer with a constant force of $8.0 \mathrm{N}$. They start out at the bottom of the slope with a speed of $5.3 \mathrm{m} / \mathrm{s}$ What is their speed at the top of the slope?

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Key Concepts

Conservation of Mechanical Energy

In the absence of non-conservative forces, the total mechanical energy (the sum of kinetic and potential energy) remains constant. However, when work is done by an applied force or against friction, the energy balance must account for these additional energy contributions or losses.

Work Done by a Constant Force

When a constant force is applied over a displacement, the work done by that force is the product of the force magnitude and the distance moved in the direction of the force. This work can either increase or decrease the object’s energy, depending on the direction of the force relative to motion.

Work-Energy Principle

This principle states that the net work done on an object is equal to its change in kinetic energy. It is used to analyze how forces acting over a distance cause changes in the motion of an object.

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. When an object is raised to a height, its potential energy increases proportionally to its mass, gravitational acceleration, and the height gained.

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