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Ch. 08 - Conservation of Energy
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoGiancoli Douglas 5th editionCh. 08 - Conservation of EnergyProblema 35
Capitolo 8, Problema 35

You slide down an 8.0-m-high icy hill (≈ frictionless). At the bottom is a level stretch where the coefficient of kinetic friction is 0.30. How far would you travel across the level stretch?

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Determine the potential energy at the top of the hill using the formula: Ui = mgh, where m is the mass of the object, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the hill (8.0 m).
At the bottom of the hill, all the potential energy is converted into kinetic energy. Use the conservation of energy principle: Ui = Kf, where Kf = (1/2)mv². Solve for the velocity v at the bottom of the hill.
On the level stretch, the kinetic energy is dissipated by the work done against friction. The work-energy principle states: Kf = W, where W = f_k d. Here, f_k is the kinetic friction force and d is the distance traveled.
Calculate the kinetic friction force using the formula: f_k = \, \(\mu\)_k \(\cdot\) m \(\cdot\) g, where \(\mu\)_k is the coefficient of kinetic friction (0.30).
Combine the equations to solve for the distance d: d = \(\frac{(1/2)mv^2}{\mu_k \cdot m \cdot g}\). Notice that the mass m cancels out, simplifying the calculation. Substitute the known values to find d.

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Concetti chiave

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Potential Energy

Potential energy is the energy stored in an object due to its position in a gravitational field. In this scenario, as you slide down the 8.0-m-high hill, gravitational potential energy is converted into kinetic energy. The initial potential energy can be calculated using the formula PE = mgh, where m is mass, g is the acceleration due to gravity, and h is the height.
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Potential Energy Graphs

Kinetic Energy and Energy Conservation

Kinetic energy is the energy of an object in motion, given by the formula KE = 0.5mv². As you descend the hill, the potential energy converts into kinetic energy, and at the bottom, all potential energy is transformed into kinetic energy. The principle of conservation of energy states that the total energy in a closed system remains constant, allowing us to equate the potential energy at the top with the kinetic energy at the bottom.
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Conservation Of Mechanical Energy

Friction and Deceleration

Friction is a force that opposes motion between two surfaces in contact. On the level stretch, the coefficient of kinetic friction (0.30) determines the frictional force acting against your motion. This frictional force causes deceleration, which can be calculated using Newton's second law (F = ma), allowing us to determine how far you will slide before coming to a stop.
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Static Friction & Equilibrium
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Consider the track shown in Fig. 8–39. The section AB is one quadrant of a circle of radius 2.0 m and is frictionless. B to C is a horizontal span 3.0 m long with a coefficient of kinetic friction μₖ = 0.25. The section CD under the spring is frictionless. A block of mass 1.0 kg is released from rest at A. After sliding on the track, it compresses the spring by 0.20 m. Determine the thermal energy produced as the block slides from B to C.

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