A 12 V car battery is found to be capable of storing 2.00 kWh of electrical energy. For a certain electric car, it is necessary to develop 1.00 x 104 W of power to drive at 5.56 m/s.
(a) Suppose that the car has 10 such batteries which results in 10 times the energy. How long (in hours) could it run if all 10 of them released all of their energy?
(b) How far (in kilometers) can the car go on its 10 batteries if they are fully charged?
a. Energy stored = 10 * 2kWh = 20 kWh.
1.00*10^4 W. = 10.*10^3 W. = 10kW.
10*h = 20
h = 2 hours. = 7200 s.
b. d = V*T = 5.56 * 7200 = 40,032 m. = 40.03 km.
(a) Well, let's start by calculating the total energy stored by these 10 batteries. Since each battery has a capacity of 2.00 kWh, the total energy would be 10 times that. So, 2.00 kWh x 10 = 20.00 kWh.
Now, to find out how long the car could run for, we need to know the power it requires. The power required to drive the car is given as 1.00 x 104 W.
Since power is the rate at which energy is used, we can calculate the time it would take for the car to use up all the energy stored in the batteries by dividing the total energy by the power.
So, 20.00 kWh / 1.00 x 104 W = 20,000 Wh / 10,000 W = 2 hours.
Therefore, the car could run for 2 hours if all 10 batteries released all of their energy.
(b) To find out how far the car can go on its 10 fully charged batteries, we need to know the energy efficiency of the car. Without that information, I can't give you a precise answer. But hey, here's a fun fact instead: Did you know that the average clown car can go really far on just a single rubber chicken? It's quacktastic!
To answer these questions, we need to use the formulas relating power, energy, voltage, and time. Here's how to get the answers step by step:
(a) To find out how long the car could run if all 10 batteries released all of their energy, we first need to determine the total energy stored in the batteries.
Given:
- Voltage of each battery (V) = 12 V
- Energy stored in one battery (E) = 2.00 kWh
The total energy stored in 10 batteries is obtained by multiplying the energy of one battery by the number of batteries:
Total Energy (E_total) = E x 10
E_total = (2.00 kWh) x 10
E_total = 20.00 kWh
Now, we need to convert the energy from kilowatt-hours (kWh) to watt-hours (Wh) since power is measured in watts:
1 kWh = 1000 Wh
E_total = 20.00 kWh x 1000 Wh/kWh
E_total = 20,000 Wh
To find the time it could run, we'll use the formula:
Time (T) = Energy (E) / Power (P)
Plugging in the values we have:
T = E_total / P
T = 20,000 Wh / (1.00 x 104 W)
Now we need to convert watt-hours to hours since power is measured in watts and time is measured in hours:
1 Wh = 1 W x 1 hour
T = 20,000 Wh / (1.00 x 104 W x 1 hour/W)
T = 2.00 hours
Therefore, the car could run for 2.00 hours if all 10 batteries released all of their energy.
(b) To find out how far the car can go on its 10 batteries, we need to use the formula relating energy, power, and time.
Given:
- Power (P) = 1.00 x 104 W
- Velocity (v) = 5.56 m/s
To find the distance (d) traveled, use the formula:
d = (P x t) / (m x v)
Where:
- t is the time in seconds
- m is the mass of the car (which is not provided)
Since we have the power (P) and the velocity (v), we can rearrange the formula to solve for time (t):
t = (d x m x v) / P
With this formula, we can't directly calculate the distance traveled using energy and power because the mass (m) of the car is not given. Additional information is required, such as the acceleration or mass of the car.
Please provide the necessary additional information, and I'll be happy to help you calculate the distance the car can go on its 10 batteries.
To find the answers to these questions, we will use the following formulas:
(a) Energy = Power x Time
(b) Energy = Power x Time = Power x (Distance / Speed)
(a) Let's calculate the total energy stored in the 10 batteries:
Total Energy = 2.00 kWh x 10 = 20.00 kWh
To find the time, we need to convert the energy from kilowatt-hours to watt-hours:
20.00 kWh = 20,000 watt-hours
Now, we can use the formula Energy = Power x Time to calculate the time:
20,000 watt-hours = 1.00 x 10^4 W x Time
Solving for Time, we get:
Time = 20,000 watt-hours / (1.00 x 10^4 W)
Time = 2 hours
Therefore, the car can run for 2 hours if all 10 batteries release all of their energy.
(b) To find the distance that the car can go on its 10 batteries, we need to divide the total energy stored in the batteries by the power required to drive the car at the given speed.
Distance = (Total Energy) / (Power / Speed)
Distance = (20,000 watt-hours) / (1.00 x 10^4 W / 5.56 m/s)
Simplifying the equation, we get:
Distance = 20,000 watt-hours / 1.80 x 10^4 W
Converting watt-hours to kilowatt-hours by dividing by 1000, we get:
Distance = 20 kWh / 18 kW = 1.11 km
Therefore, the car can go approximately 1.11 kilometers on its 10 batteries if they are fully charged.