Battery Energy and Altitude Change

[gates040]

Homework Statement

An electric scooter has a battery capable of supplying 120 Wh of energy. If friction forces and other losses acount for 60.0% of energy usage, what altitude change can a rider achieve when driving in hilly terrain, if the rider and scooter have a combined weight of 890N.

Homework Equations

Not sure...

The Attempt at a Solution

I just don't understand...

 

[gates040]

Any equations or anything that may make it clear to me would be appreciated. I am capable of solving it for myself, so it is not necessary to actually do the problem. Thank you!

 

[thomate1]

I can provide an explanation for the relationship between battery energy and altitude change. The battery in an electric scooter is responsible for supplying the energy needed to overcome the gravitational potential energy required for an altitude change. In other words, the battery provides the power needed to move the rider and scooter against the force of gravity.

In this scenario, the battery has a capacity of 120 Wh, which means it can supply 120 joules of energy for every hour of use. However, due to friction and other losses, only 40% of this energy (60% loss) is actually used for the altitude change. This means that the usable energy for the altitude change is 48 Wh (120 Wh x 0.4 = 48 Wh).

To calculate the altitude change that can be achieved, we can use the formula for potential energy: PE = mgh, where m is the mass, g is the gravitational acceleration (9.8 m/s²), and h is the altitude change. In this case, the mass is the combined weight of the rider and scooter, which is 890N. We can convert this to kilograms (kg) by dividing by the gravitational acceleration (890N / 9.8 m/s² = 90.8 kg).

Now, we can rearrange the formula to solve for h: h = PE / mg. Plugging in the values, we get h = (48 Wh x 3600 s) / (90.8 kg x 9.8 m/s²) = 197.9 meters. This means that the rider can achieve an altitude change of 197.9 meters when driving in hilly terrain.

In summary, the usable energy from the battery, combined with the weight of the rider and scooter, determines the altitude change that can be achieved. In real-world scenarios, other factors such as wind resistance and road conditions may also affect the energy usage and altitude change.