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A car with a mass of 1000 kg experiences a frictional force of 3500 N while driving at a constant speed of a 15 m/s. What is the power output of the car’s engine? (A) 3.5 kW (B) 5.25 kW (C) 35.0 kW (D) 52.5 kW

Short Answer

Expert verified
Therefore, the power output of the car’s engine is \(52.5\,kW\) (Answer D).

Step by step solution

01

Identify the Given Values

In the exercise, the mass of the car \(m = 1000\,kg\), the frictional force \(F = 3500\,N\), and the car's constant speed \(v = 15\,m/s\). These values will be used to solve the problem.
02

Apply Physics Concepts

The power \(P\) required to maintain constant speed against a frictional force is given by the formula \(P = F \cdot v\), where \(F\) is the force, and \(v\) is the velocity.
03

Calculate the Power Output

Substitute the given values into the formula, we get \(P = 3500\,N \cdot 15\,m/s = 52500\,W\). The power is often expressed in kilowatts, so we need to convert it by dividing by 1000: \(P = 52500\,W / 1000 =52.5\,kW\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Physics Problem Solving
Mastering physics problems begins with a clear understanding of the principles at play and involves a systematic approach to applying these principles to find a solution. When tackling a physics question, such as calculating the power output of a car's engine, the first crucial step is to gather all the given information from the problem, which often includes quantities like mass, force, velocity, or acceleration. In our car scenario, we have the mass of the car, the frictional force working against it, and its constant velocity.

Once the relevant information is recognized, we apply specific physics principles or formulas that relate to the context of the problem. For the car in question, we consider the concept of power related to the work done against the force of friction over some time. Physics problem-solving is not only about numbers but also about understanding how different concepts link together to affect the outcome and knowing which formulas are appropriate in a given situation.
Frictional Force
In physics, frictional force plays a significant role in the motion of objects. This force acts opposite to the direction of motion and entails the resistance that one surface or object encounters when moving over another. It is crucial in our context as it affects the power output required by a car's engine to maintain steady velocity.

In our car example, the frictional force of 3500 N is the resistive force that must be overcome to keep the car moving at a constant speed. Understanding how frictional force is calculated and how it interacts with other forces is key. While it may appear as a hindrance, friction is also essential for the car's tires to grip the road, allowing acceleration and deceleration. Recognizing the dual role of friction—as an obstacle to movement and as an aid—is fundamental to correct problem-solving in various physics scenarios.
Power Calculation
Calculating the power output of a machine or engine is a common problem in physics requiring a clear grasp of the concept of power. Power is defined as the rate at which work is done or energy is transferred. It's given by the equation \( P = F \cdot v \) where \( P \) is power in watts, \( F \) is the force in newtons, and \( v \) is the velocity in meters per second.

In the case of the car with a frictional force of 3500 N moving at a constant speed, we calculate power by multiplying force and velocity. This gives us a power output of 52500 watts, or 52.5 kilowatts when converted appropriately. Knowing how to convert units, like watts to kilowatts, is also essential in power calculations. This conversion is often required because different contexts may call for different units of measurement, making it an integral part of physics problem-solving.

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Most popular questions from this chapter

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