An electric wheel chair is designed to run on a singe 7-V battery rated to provide 87-Axh. If the wheelchair experiences an average total retarding force (mainly friction) of 150-N, how far in meters can the wheelchair travel in one charge?
To calculate the distance the wheelchair can travel in one charge, we can use the equation:
d = (E / F) * 1000
where:
- d is the distance traveled (in meters)
- E is the energy stored in the battery (in watt-hours)
- F is the retarding force (in newtons)
First, let's calculate the energy stored in the battery:
E = V * I
where:
- V is the battery voltage (in volts)
- I is the battery current (in amperes)
Given that the voltage (V) is 7 V and the battery rating is 87 A*h, we need to convert the current from ampere-hours (A*h) to amperes (A).
1 A*h = 3600 C (coulombs)
So, the battery current (I) is calculated as follows:
I = 87 A*h * 3600 C/A*h = 313200 C
Now, we can calculate the energy stored in the battery:
E = V * I = 7 V * 313200 C = 2192400 J (joules)
Next, we can use the equation mentioned earlier to find the distance traveled:
d = (E / F) * 1000 = (2192400 J / 150 N) * 1000 = 14616 m
Therefore, the wheelchair can travel approximately 14616 meters in one charge.
To calculate the distance the electric wheelchair can travel, we need to use the formula:
Distance (d) = Work (W) / Force (F)
The work done by the battery can be calculated using the formula:
Work (W) = Voltage (V) * Current (I) * time (t)
In this case, the voltage is given as 7V, and the current is given as 87 A (amperes) multiplied by the time in hours. Therefore, we need to convert the time to hours.
The retarding force experienced by the wheelchair is given as 150 N. This force works opposite to the wheelchair's motion, and it s its movement.
First, we need to convert the current from ampere-hours (Ahr) to ampere-seconds (As) for consistency:
Current (I) = 87 A * 3600s (to convert from hours to seconds)
Current (I) = 87 A * 3600s = 313,200 As
Now, we can calculate the work done by the battery:
Work (W) = Voltage (V) * Current (I) * time (t)
Work (W) = 7V * 313,200 As (since the time is in seconds)
Next, we divide the work by the retarding force to find the distance:
Distance (d) = Work (W) / Force (F)
Distance (d) = (7V * 313,200 As) / 150 N
Simplifying the equation, we have:
Distance (d) = (7 * 313,200 s) / 150
Calculating further:
Distance (d) = 2192400 s / 150
Distance (d) = 14,616 m
Therefore, the electric wheelchair can travel approximately 14,616 meters (or 14.6 kilometers) on a single charge.