Forces and Power: 18.5 HP to Drive 2320 kg Auto at 62.0 km/h

[odie5533]

Homework Statement

(A) If 18.5 HP are required to drive a 2320 kg automobile at 62.0 km/h on a level road, what is the total retarding force due to friction, air resistance, and so on?
(B) What power is necessary to drive the car at 62.0 km/h up a 15% grade (a hill rising 15.0m vertically in 100m horizontally).

The Attempt at a Solution

18.5 HP = 13795 W
62.0 km/h = 17 m/s
A) $$P = F*v$$
$$P / v = F$$
$$F = ma$$
$$P / v = ma$$
$$a = P / (v * m)$$
$$13795 / (17 * 2320) = 0.3498N$$
B) $$\alpha = arctan(15/100) = 8.53$$
$$\sum F = F_{up} - 0.3498N - w sin(8.530)$$
$$\sum F = F_{up} - 0.3498N - 3375N$$
$$F_{up} = 3375N$$
$$P = F * v$$
$$P = 3375 * 17 = 57375 W = 77 HP$$

This seems completely wrong to me... I'm not sure if any of it is right even. Any help would be greatly appreciated.

 

[learningphysics]

Your part a) isn't right. You had the right formula, but didn't use it. F = P/v.

plug in P plug in v. get F.

Part b), your work is right... you just need to use the correct force from part a).

 

[odie5533]

Thanks learningphysics! I had no idea I was so close to the answer, I figured all my work was wrong :(