How Much Power Does a Car Need to Climb a Hill at 100 km/h?

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Homework Help Overview

The problem involves calculating the power required for a car to maintain a speed of 100 km/h while climbing a hill with a slope of 3.50°. The context includes considerations of gravitational force and aerodynamic drag, with specific parameters provided for the car's mass, drag coefficient, and frontal area.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate the total force required to overcome both gravitational and aerodynamic forces, leading to a power calculation. Some participants question the accuracy of the original poster's calculations and suggest verifying the problem's given information.

Discussion Status

The discussion is ongoing, with some participants expressing confidence in the original poster's calculations while others suggest there may be an error in the interpretation or transcription of the problem data. There is a recognition of a potential discrepancy in the expected answer.

Contextual Notes

Participants are considering the accuracy of the parameters provided in the homework statement, including the drag coefficient and the slope of the hill, as well as the implications of rounding or approximation in their calculations.

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Homework Statement


The mass of a car is 1500 kg. The shape of the body is such that its aerodynamic drag coefficient is D = 0.380 and frontal area is 2.50 m2. Assuming that the drag force is proportional to v^2 and ignoring other sources of friction, calculate the power required to maintain a speed of 100 km/h as the car climbs a long hill sloping at 3.50° the answer is in horsepower


Homework Equations


R = .5DpAv^2
P = Fv
1hp = 746W


The Attempt at a Solution


Total force the engine needs to overcome is the gravitational force at an angle and air resistance.
To find force, F = mgsin(theta) + .5 DpAv^2. Plugs everything in, F = (1500)(9.8)sin(3.5) + .5(.38)(1.29)(2.5)(27.78^2) = 1370.3N
To find power, P = 1370.3(27.78) = 38067W, 38067W = 51 hp.

I don't think my answer is correct. Can anyone offer any insight as to why? Thank you in advance.
 
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Looks correct to me. You probably were expecting a bit more horse required?
 
I entered my answer into the online homework thing and it told me I was 10% within the correct answer. I just can't figure out what's wrong with what I did. Man...
 
Did you copy down the correct information given in the problem?
 

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