A popular carnival ride consists of seats attached to a central disk through cables. The p...

SKETCH:

The sketch for carnival ride is shown in the below figure.

RESEARCH:

The tension force acting on the cable is resolved into the horizontal and vertical components. Now, the horizontal component of the tension force provides the centripetal force (), which is acting towards the center of the carnival. So, the horizontal component of the tension is

The centripetal force acting on the passenger is given by the equation

Here and are the mass and the speed of the passenger and is the radius of the passenger orbit.

Therefore, the horizontal component of the tension force will be equal to

…… (1)

Now, the vertical component of tension force on the cable is equal to the weight of the passenger. Hence the vertical component of tension force is

…… (2)

Here is the acceleration due to gravity.

SIMPLIFY:

Using equations (1) and (2), we get the speed of the passenger

From the above diagram, the radius of the passenger orbit is given by

Hence, the above equation becomes as

…… (3)

Here is the length of the cable and is the radius of the central disk.

Given data:

The radius of the central disk,

The length of the cable,

The mass of the passenger,

The angle of the cable with the cable,

The acceleration due to gravity,

CALCULATE:

(a)

Now, substituting the numerical values in the equation (3), we get the speed of the passenger

Now, substituting the numerical values in the equation (2), we get the force exerted by the cable on the chair (Tension force)