本题目来源于试卷: 2012美国US F=MA物理竞赛，类别为 美国F=MA物理竞赛
[单选题]
A car of mass $m$ has an engine that provides a constant power output $P$. Assuming no friction, what is the maximum constant speed $v_{max}$ that this car can drive up a long incline that makes an angle $\theta$ with the horizontal?
A. $v_{max} = P / (mg \sin \theta)$
B. $v_{max} = P^{2} \sin \theta / mg$
C. $v_{max} = \sqrt{2P / mg} / \sin \theta$
D. There is no maximum constant speed.
E. The maximum constant speed depends on the length of the incline.
参考答案: A
本题详细解析:
To move at a constant 6 o //kozu;z 0o*4m+ lr hsuubuurdt17speed $v_{max}$, the net force must be zero. The engine's forward force $F_{engine}$ must balance the component of gravity pulling the car down the incline, $F_{gravity} = mg \sin \theta$.
So, $F_{engine} = mg \sin \theta$.
Power is defined as $P = F \cdot v$.
At maximum constant speed, $P = F_{engine} \cdot v_{max}$.
$P = (mg \sin \theta) v_{max}$.
Solving for $v_{max}$ gives $v_{max} = \frac{P}{mg \sin \theta}$.
| 
