In a children's park, there is a slide which has a total...

In a children's park, there is a slide which has a total length of $10 \mathrm{~m}$ and a height of $8 \cdot 0 \mathrm{~m}$ (figure 8 -E3). Vertical ladder are provided to reach the top. A boy weighing $200 \mathrm{~N}$ climbs up the ladder to the top of the slide and slides down to the ground. The average friction offered by the slide is three tenth of his weight. Find (a) the work done by the boy on the ladder as he goes up, (b) the work done by the slide on the boy as he comes down, (c) the work done by the ladder on the boy as he goes up. Neglect any work done by forces inside the body of the boy.

In a children's park, there is a slide which has a total length of $10 \mathrm{~m}$ and a height of $8 \cdot 0 \mathrm{~m}$ (figure 8 -E3). Vertical ladder are provided to reach the top. A boy weighing $200 \mathrm{~N}$ climbs up the ladder to the top of the slide and slides down to the ground. The average friction offered by the slide is three tenth of his weight. Find
(a) the work done by the boy on the ladder as he goes up,
(b) the work done by the slide on the boy as he comes down, (c) the work done by the ladder on the boy as he goes up. Neglect any work done by forces inside the body of the boy.

Key Concepts

Force Components and Work Direction

The concept of force components is important when analyzing work done by forces that are not aligned with the displacement. Only the component of the force parallel to the displacement does work. This is critical in understanding why, for example, a normal force or a perpendicular reaction force (such as that provided by a ladder) does no work.

Friction

Friction is a non-conservative force that opposes the relative motion of surfaces in contact. It does negative work since it acts in the direction opposite to displacement, converting mechanical energy into thermal energy. In energy analysis, considering friction is essential to understand energy losses during motion, such as sliding down a slope.

Gravitational Potential Energy

Gravitational potential energy is the energy stored by an object due to its position in a gravitational field. When an object is raised to a higher elevation, work is done against gravity, which results in an increase in its gravitational potential energy. This concept is crucial when calculating the work done to elevate an object like a person climbing a ladder.

Work

Work is defined as the dot product of force and displacement. It quantifies the energy transfer when a force causes an object to move. In physics problems involving motion along a path, work helps in understanding how different forces contribute to changes in energy, such as increasing potential energy when climbing or being dissipated as heat due to friction.

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