Chapter 10, Problem 47A

The sketch shows a conical pendulum. The bob swings in a circular path. The tension T and weight W are shown by vectors. Draw a parallelogram with these vectors and show that their resultant lies in the plane of the circle (recall the parallelogram rule in Chapter 5). What name do we use for this resultant force?

To determine

To draw: The sketch of a parallelogram with the vectors T and W along with their resultant.

To find: The name for the resultant force.

Answer to Problem 47A

The sketch is shown in Figure 1.

The resultant force is the centripetal force lies in the plane of circle.

Explanation of Solution

Introduction:

The centripetal force of the object is defined as,

  $F_{\text{c}}=\frac{m{v}^2}{r}$

Here, $m$ is the speed, $v$ is the speed, and $r$ is the radius of curvature.

Calculation:

Consider the tension T and weight W are the two adjacent sides of the parallelogram for the bob swings in a circular path.

Draw the sides of a parallelogram by draw a parallel to the force vectors tension T and weight W.

Sketch the parallelogram of forces as shown below.

  

Figure 1

The resultant force of the tension T and weight W is $F_{\text{c}}$ .

The resultant force $F_{\text{c}}$ represents centripetal force that lies on the plane of circle.

Hence, the resultant force is the centripetal force lies in the plane of circle.

Conclusion:

Thus, the resultant force is the centripetal force lies in the plane of circle.