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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 64
Capitolo 9, Problema 64

A farmer uses a tractor to pull a 150 kg bale of hay up a 15° incline to the barn at a steady 5.0 km/h. The coefficient of kinetic friction between the bale and the ramp is 0.45. What is the tractor's power output?

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Step 1: Identify the forces acting on the bale. These include the gravitational force (mg), the normal force, the frictional force, and the force exerted by the tractor. The gravitational force can be broken into two components: one parallel to the incline (m * g * sin(θ)) and one perpendicular to the incline (m * g * cos(θ)).
Step 2: Calculate the normal force. The normal force is equal to the perpendicular component of the gravitational force, which is given by: F_normal = m * g * cos(θ). Use the mass of the bale (150 kg), the gravitational acceleration (g = 9.8 m/s²), and the incline angle (15°).
Step 3: Determine the frictional force. The frictional force is given by: F_friction = μ_k * F_normal, where μ_k is the coefficient of kinetic friction (0.45). Substitute the value of the normal force calculated in Step 2 to find F_friction.
Step 4: Calculate the total force required to pull the bale up the incline at a constant velocity. Since the bale is moving at a steady speed, the net force is zero. Therefore, the tractor's force must balance the sum of the parallel component of gravity (m * g * sin(θ)) and the frictional force (F_friction).
Step 5: Compute the power output of the tractor. Power is given by: P = F_total * v, where F_total is the total force calculated in Step 4 and v is the velocity of the bale (5.0 km/h, converted to m/s). Substitute the values to find the power output.

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Concetti chiave

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Power

Power is defined as the rate at which work is done or energy is transferred over time. In physics, it is calculated as the work done divided by the time taken. The unit of power is the watt (W), where 1 watt equals 1 joule per second. Understanding power is essential for determining how much energy the tractor uses to pull the bale up the incline.
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Power

Work and Energy

Work is the product of the force applied to an object and the distance over which that force is applied, in the direction of the force. In this scenario, the work done by the tractor includes overcoming gravitational forces and friction as it pulls the bale up the incline. The concept of energy conservation is also relevant, as the work done translates into kinetic and potential energy changes.
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The Work-Energy Theorem

Friction

Friction is the resistive force that opposes the motion of an object in contact with a surface. The coefficient of kinetic friction quantifies this resistance and is crucial for calculating the force needed to move the bale up the incline. In this problem, the frictional force must be considered alongside gravitational forces to determine the total force exerted by the tractor.
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Static Friction & Equilibrium
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A Porsche 944 Turbo has a rated engine power of 217 hp. 30% of the power is lost in the engine and the drive train, and 70% reaches the wheels. The total mass of the car and driver is 1480 kg, and two-thirds of the weight is over the drive wheels. If the Porsche accelerates at amax, what is its speed when it reaches maximum power output?

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