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Ch 09: Work and Kinetic Energy
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 09: Work and Kinetic EnergyProblema 49a
Capitolo 9, Problema 49a

A 50 kg ice skater is gliding along the ice, heading due north at 4.0 m/s. The ice has a small coefficient of static friction, to prevent the skater from slipping sideways, but μk = 0. Suddenly, a wind from the northeast exerts a force of 4.0 N on the skater. Use work and energy to find the skater's speed after gliding 100 m in this wind.

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Step 1: Identify the forces acting on the skater. The skater is initially moving due north with a velocity of 4.0 m/s. The wind exerts a force of 4.0 N from the northeast, which has both northward and eastward components. Since μₖ = 0, there is no kinetic friction acting on the skater.
Step 2: Resolve the wind force into its components. The northeast direction implies a 45° angle relative to the north and east axes. Use trigonometric functions to find the components of the force: Fₙ = F * cos(45°) and Fₑ = F * sin(45°), where F = 4.0 N.
Step 3: Calculate the work done by the wind force in the northward direction. Work is given by W = Fₙ * d, where Fₙ is the northward component of the force and d = 100 m is the distance traveled. This work contributes to the change in kinetic energy of the skater.
Step 4: Apply the work-energy theorem. The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy: W = ΔKE = KE_final - KE_initial. The initial kinetic energy is KE_initial = (1/2) * m * v², where m = 50 kg and v = 4.0 m/s. The final kinetic energy is KE_final = (1/2) * m * v_final².
Step 5: Solve for the final speed v_final. Rearrange the work-energy equation to find v_final: v_final = sqrt((2 * W / m) + v²). Substitute the values for W, m, and v to determine the skater's final speed after gliding 100 m in the wind.

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Work-Energy Principle

The Work-Energy Principle states that the work done on an object is equal to the change in its kinetic energy. In this scenario, the wind exerts a force on the skater, doing work on her as she glides. This work will increase her kinetic energy, which can be calculated using the formula W = F × d, where W is work, F is the force applied, and d is the distance moved in the direction of the force.
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The Work-Energy Theorem

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, given by the formula KE = 0.5 × m × v², where m is mass and v is velocity. In this problem, the skater's initial kinetic energy can be calculated using her mass and initial speed. After the wind does work on her, her final kinetic energy will reflect her increased speed, allowing us to find the new velocity.
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Intro to Rotational Kinetic Energy

Friction and Motion

Friction is a force that opposes the relative motion of two surfaces in contact. In this case, the ice has a small coefficient of static friction, which means it allows the skater to glide without slipping sideways. However, since the problem states that μₖ = 0, we can ignore kinetic friction, simplifying our calculations as the skater's motion is primarily influenced by the wind's force.
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Kinetic Friction Problems
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