# Electric car and battery problem

• ddobre
In summary: I'm going to go take a break and try to come back to this later.In summary, the electric car can travel 410.4 kilometers before needing to be recharged.
ddobre

## Homework Statement

An electric car (mass 1560 kg) draws power from a set of 24 batteries. Each battery supplies 12 V, with storage 95 A·h. During a test of the vehicle, it is driven at exactly 45 km/h on a level road while experiencing a friction force of 240 N.
(a) What is the horsepower required during this test?
(b) Neglecting all other forms of energy loss (e.g. inefficiencies, acceleration), how many kilometers can the car travel before the batteries need to be recharged?

## Homework Equations

P = A*V
1hp = 746w
P = F*v(velocity)

## The Attempt at a Solution

The first thing I did was add up all the batteries voltages. Next I multiplied that value by the 95A*h rating to get P(watts) = 27360w*h. Next, I converted the speed from km/h to m/s: 12.5 m/s. Lastly, I tried finding the power of the frictional force on the car via P = F*v, (P = 240N * 12.5 m/s), and got 3000w. As a way of relating things, I wrote 27360w in terms of hp: 36.68hp. The part I am confused about is how I should be relating the frictional force to the horsepower required, and I'm also a little confused about the units of power I calculated for the frictional force. I have not thought about part b) yet. Any advice?

ddobre said:
I wrote 27360w in terms of hp
Why? You do not have a quantity 27360W.
ddobre said:
how I should be relating the frictional force to the horsepower required
Is there any acceleration?
ddobre said:
confused about the units of power I calculated for the frictional force
You wrote
ddobre said:
P = 240N * 12.5 m/s
so it's Nm/s, also known as ?

haruspex said:
Why? You do not have a quantity 27360W.

Is there any acceleration?

You wrote

so it's Nm/s, also known as ?

Right, the quantity of have is 27360 w*h, not watts. There should be no acceleration on the car since it moves at a constant speed. I knew it was in terms of watts, but I am still unsure of how I should factor that in in terms of how much power is getting taking from the batteries simply due to friction.

ddobre said:
Right, the quantity of have is 27360 w*h, not watts. There should be no acceleration on the car since it moves at a constant speed. I knew it was in terms of watts, but I am still unsure of how I should factor that in in terms of how much power is getting taking from the batteries simply due to friction.
Think about the forces. What rate of work is friction doing against the car?

haruspex said:
Think about the forces. What rate of work is friction doing against the car?

That should be W = F*d, so that would be W = (240N) * (45000m) = 1.08x10^7 Joules

ddobre said:
That should be W = F*d, so that would be W = (240N) * (45000m) = 1.08x10^7 Joules
I wrote "rate of work", i.e. power.

haruspex said:
I wrote "rate of work", i.e. power.

Okay, so a force of 240N acting on the car as it travels at 12.5 m/s: P = 3000 Nm/s.

ddobre said:
Okay, so a force of 240N acting on the car as it travels at 12.5 m/s: P = 3000 Nm/s.
Right, so to maintain a steady speed, what power does the engine need to deliver?

haruspex said:
Right, so to maintain a steady speed, what power does the engine need to deliver?

If it provides 3000 Nm/s, then it would be equal to the frictional power. If the engine uses a larger amount of power than 3000 Nm/s, it would accelerate (?) So the engine needs to produce power equivalent to the rate of work of friction on it.

ddobre said:
If it provides 3000 Nm/s, then it would be equal to the frictional power. If the engine uses a larger amount of power than 3000 Nm/s, it would accelerate (?) So the engine needs to produce power equivalent to the rate of work of friction on it.
Right.

Okay, that cleared some things up for me. For the second part I know I have to calculate the distance using the power of the batteries, but the units for the battery is w*h, so I'm thinking I could convert that to watts per second and then divide by the power needed by the engine to get the distance traveled. But I think that leaves the units in seconds, which is not quite what I'm looking for. But if I used V = d/t, then solve for d, then maybe this could work. I am getting a value of 410.4 km as the distance the car can travel.

ddobre said:
convert that to watts per second
You mean watt-seconds, = J.
ddobre said:
410.4 km
Right.
Or more simply, work = F x d, where F=240N, work = 27360w*h.

haruspex said:
You mean watt-seconds, = J.

Right.
Or more simply, work = F x d, where F=240N, work = 27360w*h.

Ah yes that would be a much simpler solution than my method. This has been a lot of help, thanks. I don't get to talk to my professor or other students in the class very often.

## 1. What is the main problem with electric cars?

The main problem with electric cars is their limited driving range. Most electric cars can only travel around 200-300 miles on a single charge, while traditional gasoline cars can travel up to 400-500 miles on a full tank.

## 2. How long do electric car batteries last?

The lifespan of an electric car battery can vary depending on the type of battery and usage. Generally, they are expected to last around 8-10 years or 100,000 miles. However, advancements in battery technology are continuously being made to improve their lifespan and efficiency.

## 3. Can electric car batteries be recycled?

Yes, electric car batteries can be recycled. In fact, most manufacturers have programs in place to recycle old batteries. The materials in the batteries, such as lithium and cobalt, can be reused in new batteries or other products.

## 4. How long does it take to charge an electric car?

The time it takes to charge an electric car can vary depending on the type of charger and the car's battery size. On average, it can take anywhere from 30 minutes to 12 hours to fully charge an electric car. However, with advancements in fast charging technology, some cars can now charge up to 80% in just 20 minutes.

## 5. Are electric cars more expensive to maintain than traditional cars?

Overall, electric cars tend to have lower maintenance costs compared to traditional cars. This is because they have fewer moving parts and do not require regular oil changes or tune-ups. However, the cost of battery replacement can be a significant expense for electric car owners.

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