PROBLEM
(II) What is the minimum work needed to push a 950−kg car 510 m up along a 9.0∘ incline? Ignore friction.
STEP 1
1. The car has a mass of 950kg.
2. The incline is 9.0∘.
3. The distance along the incline is 510m.
4. Friction is ignored.
5. Work is calculated as the force parallel to the incline times the distance.
STEP 2
1. Determine the gravitational force acting on the car.
2. Calculate the component of the gravitational force parallel to the incline.
3. Calculate the work done to move the car up the incline.
STEP 3
Determine the gravitational force acting on the car:
Fgravity=m⋅g where m=950kg and g=9.8m/s2.
Fgravity=950kg×9.8m/s2=9310N
STEP 4
Calculate the component of the gravitational force parallel to the incline:
Fparallel=Fgravity⋅sin(θ) where θ=9.0∘.
Fparallel=9310N⋅sin(9.0∘) Calculate sin(9.0∘):
sin(9.0∘)≈0.1564 Fparallel=9310N×0.1564≈1456N
SOLUTION
Calculate the work done to move the car up the incline:
W=Fparallel⋅d where d=510m.
W=1456N×510m W≈742560J The minimum work needed to push the car up the incline is:
742560J
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