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

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To calculate the power needed for a car weighing 1500 kg to climb a 3.5° hill at 100 km/h, the total force includes gravitational force and aerodynamic drag. The gravitational force is calculated using F = mgsin(theta), while drag is determined by the formula R = 0.5DpAv^2. The total force amounts to 1370.3 N, leading to a power requirement of 38,067 W, which converts to approximately 51 horsepower. Despite this calculation, there is uncertainty about the accuracy of the answer, with indications that it may be within 10% of the correct value. Clarification on the problem's parameters could help resolve the discrepancy.
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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?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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