Final answer:
To find the strain on the brakes, we calculate the component of the car's weight along the slope, which requires converting the slope angle to decimal degrees and using the sine function.
Step-by-step explanation:
The question asks us to calculate the strain imposed on the brakes of an automobile, which weighs 2,000 lbs., that is held stationary on a hill with a slope of 20°30'. The strain on the brakes is equivalent to the component of the car's weight along the slope of the hill, since the car is stationary. To calculate this, we can use the component of gravity parallel to the slope.
First, we must convert the angle to decimal degrees. 20°30' is equal to 20.5 degrees. Since the car is stationary, the force of gravity along the slope (which the brakes must oppose) is:
F_parallel = weight * sin(θ) = 2,000 lbs * sin(20.5 degrees)
After calculating this value, we round it to the nearest pound to find the strain on the brakes.