Space Time & Motion A.2 Forces & Momentum (id: 35edaef51)

本题目来源于试卷: Space Time & Motion A.2 Forces & Momentum，类别为 IB物理学

[单选题]
A mass m attached to a string is moving in a horizontal circular motion as shown. The tension on the string is T, and the angle with the vertical is θ.

Which of the following statements are correct for this motion?

• I. Centripetal force = mg tan(θ).
• II.Total gravitational and kinetic energy of the mass is constant.
• III. If the rope is cut, the mass will fall downwards with a straight line trajectory.
  

A. Only I
B. I and II
C. II and III
D. II and III


参考答案:  B


本题详细解析:

$\underline{\text{Explanation}}$: 
Statement I is correct: 
$$ $T$ $cos(\theta )$ = $mg$, which gives $T=\frac{mg}{cos(\theta )}$

$$ centripetal force ($F_c$) = $T$ $sin(\theta )$

Substituting $\frac{mg}{cos(\theta )}$ for $T$ in the second equation:

$$ $F_c=mg$ $\frac{sin(\theta )}{cos(\theta )}$ = $mg$ $tan(\theta )$.

Statement II is correct: 
The path is a horizontal plane, therefore gravitational potential energy is constant. No work is done, therefore kinetic energy is constant. Total mechanical energy is constant.

Statement III is false: 
The mass has a horizontal velocity during this motion. When the rope is cut, the only force will be the weight, therefore it will move in a projectile motion starting with a horizontal velocity, following a vertical parabolic path (not fall directly downwards)

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