Nora’s car is run out of gas and she noticed that a gas station is just 125 feet away the incline road. She decided to push the car up a 14 degree inclined with a force of 250 N to get to the gas station. Determine how much work is done pushing the car to the gas station.
14J
To determine the amount of work done in pushing Nora's car up the incline, we need to calculate the work done against gravity.
The formula to calculate work is given by:
Work = Force × Distance × cos(θ)
Where:
- Force is the applied force (250 N in this case)
- Distance is the displacement (in this case, the distance of 125 feet)
- θ is the angle between the force and the direction of motion (14 degrees in this case)
However, before we can use this formula, we need to convert the distance and angle to the SI unit system (meters and radians) for consistency.
1 foot = 0.3048 meters, so 125 feet = 38.1 meters.
To convert degrees to radians, we use the conversion factor π/180.
Therefore, 14 degrees = 14 × π/180 radians ≈ 0.244 radians.
Now, we can substitute the values into the formula:
Work = 250 N × 38.1 m × cos(0.244 radians)
To calculate the cosine of 0.244 radians, we can use a calculator or a mathematical software/tool.
After calculating the cosine value, we can multiply it by the force and distance to determine the work done in pushing the car up the incline.