Space Time & Motion A.2 Forces & Momentum (id: f99b90e11)

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

[填空题]

• A conical pendulum consists of a 22cm string that makes an angle θ with the vertical as shown in the diagram.
  Mass of the bob = 8.0g
  
  Angle with the vertical θ=$20^{\circ}$
  
  
  Show that angular velocity $\omega$ is given by $\omega=\sqrt{\frac{g\tan \theta}{\tau}}$
  2.2Calculate the linear velocity of the bob   $ms^{-1}$
  
  2.3Determine the tension in the string.   N
  
  3.1Explain the effect of increasing the angular speed ω on the angle θ.
  
  3.2The maximum tension the string can provide is 1.5N. Determine the maximum angular speed.  $rads^{-1}$
  
  

参考答案:
空格1: 0.52  空格2: 0.08  空格3: 29.2 


本题详细解析:

3.1The vertical component of the tension force remains constant, as it is equal to the weight of the bob. 

$\mathrm{✓}$

The horizontal component of the tension provides the centripetal force, which increases as ω increases. $\mathrm{✓}$

Because the horizontal component increases while the vertical component stays constant, the angle θ will increase with ω $\mathrm{✓}$

Therefore centripetal force is equal to the tension force/rope is almost horizontal/θ very close to $90^o$.

$\underline{\text{Further Explanation}}$: 
Gravitational force is

mg=(0.008)(9.8)=0.08N

The maximum tension is $1.5N$, which is the resultant of the vertical component of tension (mg) and the horizontal component of the tension, $F_c$.

Therefore

$1.5^2=0.08^2+{F_c}^2$

solving gives {F_c}=1.49787=1.5

This shows that the centripetal force is effectively equal to the tension force and the string very close to horizontal.

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