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. (a) What is the maximum acceleration of the Porsche on a concrete surface where μₛ = 1.00 ? Hint: What force pushes the car forward?
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Calculate the effective power at the wheels by taking 70% of the total engine power. Use the formula: Power at wheels = 0.70 imes Total power.
Convert the power at the wheels from horsepower to watts, knowing that 1 horsepower is approximately equal to 746 watts.
Determine the force exerted by the wheels on the road using the formula: Force = Power / Velocity. Note that the maximum force occurs at the lowest speed (assuming the car starts from rest, use the initial velocity as close to zero).
Calculate the normal force acting on the drive wheels, which is two-thirds of the total weight of the car. Use the formula: Normal force = (2/3) imes (mass of car imes acceleration due to gravity).
Find the maximum acceleration using the formula: Maximum acceleration = (Force due to friction) / (Mass of the car). The force due to friction can be calculated by multiplying the normal force by the coefficient of static friction (μₛ).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Power and Efficiency
Power is the rate at which work is done or energy is transferred. In this context, the Porsche's engine produces 217 horsepower, but only 70% of this power is effectively used for acceleration due to losses in the engine and drivetrain. Understanding how power is converted into usable force is crucial for calculating the car's performance.
Friction is the force that opposes the relative motion of two surfaces in contact. The coefficient of static friction (μₛ) indicates the maximum frictional force before sliding occurs. For the Porsche on a concrete surface with μₛ = 1.00, this frictional force is essential for determining how much of the engine's power can be converted into forward acceleration.
Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = ma). In this scenario, the net force is the frictional force that propels the car forward, and understanding this relationship is key to calculating the maximum acceleration of the Porsche.