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QuestionFind the grade resistance in pounds for a 2000-pound car on a 2.4∘2.4^{\circ} uphill grade using F=Wsin⁡θF=W \sin \theta.

Studdy Solution

STEP 1

Assumptions1. The weight of the automobile (W) is2000 pounds. The grade of the hill (θ) is.4 degrees3. The force due to gravity () is calculated using the formula =Wsin⁡θ=W \sin \theta

STEP 2

First, we need to convert the grade of the hill from degrees to radians because the sin function in the formula uses radians.
θradians=θdegrees×π180\theta_{radians} = \theta_{degrees} \times \frac{\pi}{180}

STEP 3

Now, plug in the given value for the grade of the hill to calculate the grade in radians.
θradians=2.×π180\theta_{radians} =2. \times \frac{\pi}{180}

STEP 4

Calculate the grade in radians.
θradians=2.4×π180=0.04189\theta_{radians} =2.4 \times \frac{\pi}{180} =0.04189

STEP 5

Now that we have the grade in radians, we can calculate the force due to gravity () using the formula =Wsin⁡θ=W \sin \theta.

STEP 6

Plug in the values for the weight of the automobile and the grade of the hill in radians to calculate the force due to gravity.
=2000×sin⁡(0.04189) =2000 \times \sin(0.04189)

STEP 7

Calculate the force due to gravity.
=2000×sin⁡(0.04189)=83.6 =2000 \times \sin(0.04189) =83.6The grade resistance of a2000-pound car traveling on a 2.4∘2.4^{\circ} uphill grade is83.6 pounds.

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