Instead of moving back and forth, a conical pendulum moves in a circle at constant speed as its string traces out a cone (see figure below). One such pendulum is constructed with a string of length L =10.7 cm and bob of mass 0.344 kg. The string makes an angle = 5.58° with the vertical.

(a) What is the radial acceleration of the bob?
magnitude

(b) What are the horizontal and vertical components of the tension force exerted by the string on the bob? (Assume radially inward to be the positive x axis and vertically upward to be the
positive y axis. Express your answer in vector form.)
T= N

a

The  radial acceleration is  

b

The horizontal Tension is  

The vertical Tension is  

Explanation:

The diagram illustrating this is shown on the first uploaded

From the question we are told that

   The length of the string is  

     The mass of the bob is  

     The angle made  by the string is  

The centripetal force acting on the bob is mathematically represented as

Now From the diagram we see that this force is equivalent to

      where T is the tension on the rope  and v is the linear velocity  

     So

Now the downward normal force acting on the bob is  mathematically represented as

So

=>    

=>  

The centripetal acceleration which the same as the radial acceleration  of the bob is mathematically represented as

=>  

substituting values

The horizontal component is mathematically represented as

substituting value

The vertical component of  tension is  

substituting value

The vector representation of the T in term is of the tension on the horizontal and the tension on the vertical is  

substituting value  

ι вєℓιєνє ιт ιѕ тнє fιяѕт ¢нσι¢є(α.)

нє ѕнσυℓ∂ ѕмιℓє ρσℓιтℓу αи∂ ѕρєαк тσ тнє ρєяѕσи ωнσ ιѕ ιитєяяυριиg αfтєя тнє ∂ιѕ¢υѕѕισи

нσρє ι ¢συℓ∂ нєℓρ.