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Answer :
Final answer:
The equivalent gain in the loading force for the tractor and scraper when going downslope is calculated through the gravitational force. It provides an extra force to the tractor and scraper due to the downward slope, calculated to be 13,199.5 lb. This value would be subtracted from the total force if they were going uphill.
Explanation:
To calculate the equivalent gain in loading force for the tractor and scraper when going downslope, we'll use the concept of gravitational force. This force, when an object moves downhill, acts in the same direction as their motion, hence increasing the force. The gravitational force (F) can be calculated using the equation F = weight * sin(θ), where weight is the combined weight of the tractor and scraper, and θ is the slope angle.
Since we’re dealing with a 4% slope, it’s nearly equivalent to an angle of about 2.29 degrees (since we calculate θ = atan(slope percentage/100)).
Adding the weights of the tractor and scraper, we get a total weight of 333,100 lb. Inserting these values into the equation, we obtain:
F = 333,100 lb * sin(2.29)
= 13,199.5 lb.
Therefore, the equivalent gain in loading force would be 13,199.5 lb, which is the extra force provided by gravity due to going downslope. This value should be subtracted from the overall force if the scraper was being loaded uphill.
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