Consult Interactive Solution 19.5 at www.wiley.com/college/...

Consult Interactive Solution $19.5$ at www.wiley.com/college/ cutnell to review one method for modeling this problem. MultipleConcept Example 3 employs some of the concepts that are needed here. An electric car accelerates for $7.0 \mathrm{~s}$ by drawing energy from its $290-\mathrm{V}$ battery pack. During this time, $1200 \mathrm{C}$ of charge passes through the battery pack. Find the minimum horsepower rating of the car.

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Key Concepts

Unit Conversion and Horsepower

In scenarios where power output needs to be expressed in specific units, such as horsepower, unit conversion plays a critical role. One horsepower is equivalent to approximately 745.7 watts, meaning that after computing power in watts, it can be converted to horsepower to meet the required specifications in mechanical and automotive contexts.

Electric Potential Energy

This concept involves the energy stored when electrical charges move through a potential difference. In electrical systems, the work done (or energy transferred) by moving a charge Q through a voltage V is given by the product E = V × Q, which is fundamental for determining the energy output of any electrical source.

Power and Work Relationship

Power is defined as the rate at which work is done or energy is transferred. In problems involving energy consumption over time, average power is calculated by dividing the total energy by the time interval during which it is used. This is essential for linking energy supplied by a battery to the mechanical power required to perform work, such as accelerating a vehicle.

Transcript

00:01 Hi there, so for this problem we are given the time that an electric car takes to accelerate, that is seven seconds.

00:11 And we know that the battery provides a both a difference in the voltage of the voltage of 290 poles, that is the difference in potential.

00:34 And there are, during this time, 1 ,200 columns is the charge that is passing through the battery pack.

00:52 So we need to find the minimum horsepower that rating for this card.

00:58 So we need to find the power for this card.

01:07 We know that the energy to accelerate the car comes from the energy that is in store in the battery.

01:17 Now, work is done by the electric force as the charges move from point a to point b, being point a, the positive terminal and point b the negative terminal.

01:33 So the word done by the electric force is just equal to the charge that we have in this case times the difference in potential.

01:51 We can write this as this, the potential in b minus the potential in a.

01:58 Now, that value is given.

02:01 And the power that is supplied by the battery, it is the word.

02:06 Word done divided by the time.

02:08 So the power is defined as the word done divided by the time.

02:14 And we also have that time.

02:15 So what we need to do is just substitute all of these values.

02:20 I'm going to put that here...