A conical pendulum is formed by a mass of 100 g (0.1 kg) moving in a circle as shown. The string makes an angle of 30o.

1. Draw the free body force diagram.

2 Calculate the weight of the mass.

3 State the vertical component.

4 Calculate the horizontal component.

5 Calculate the tension in the string.

6 Draw and label the force vector diagram.

Success criteria:You are able to accurately draw free body force diagrams;you are able to calculate values for free body force diagrams; andyou can correctly label free body force diagrams

Take g = 9.8 m s-2

Horizontal Circular Motion - Conical pendulum

θ

Angle Weight Working out Tension N

30o 0.98 0.98 ÷ cos 30 1.1

60o 0.98

75o 0.98

85o 0.98

89o 0.98

89.9o 0.98

89.9999o 0.98

θ

Horizontal Circular Motion - Conical pendulum

A group of year 13 students were investigating the conical pendulum.

They wondered how fast you had spin the rubber bung so that it spun horizontal.

The group then thought that it might not be possible to get the bung to swing absolutely horizontal and perhaps they could prove that mathematically.

One student put 90o in his calculator and came up with error.

mass of the rubber bung is 100 g (0.1 kg)

30o ≤ θ < 90o

Complete the table below.

Draw a vector diagrams for 30o, 60o, 75o, 85o

Comment on your attempts to draw vector diagrams for 85o, 89o and 89.9o

Take g = 9.8 m s-2

Complete the table below.

Draw a vector diagrams for 30o, 60o, 75o, 85o

Comment on your attempts to draw vector diagrams for 85o, 89o and 89.9o

Angle Weightkg

Working out Tension N

30o 0.98 0.98 ÷ cos 30 1.1

60o 0.98 0.98 ÷ cos 60 2.0

75o 0.98 0.98 ÷ cos 75 3.8

85o 0.98 0.98 ÷ cos 85 11

89o 0.98 0.98 ÷ cos 89 56

89.9o 0.98 0.98 ÷ cos 89.9 560

89.9999o 0.98 0.98 ÷ cos 89.9999 560000

θ

Horizontal Circular Motion - Conical pendulum

mass of the rubber bung is 100 g (0.1 kg)

30o ≤ θ < 90o

Take g = 9.8 ms-2

A group of year 13 students were investigating the conical pendulum.

They wondered how fast you had spin the rubber bung so that it spun horizontal.

The group then thought that it might not be possible to get the bung to swing absolutely horizontal and perhaps they could prove that mathematically.

One student put 90o in his calculator and came up with error.

Vertical comp. = 0.98 N

60o

Scale : 5.0 cm = 1 N

Tension = 2.0 N

Horizontal Circular Motion - Conical pendulum

Scale : 5.0 cm = 1 N

30oTension = 1.1 N

Vertical comp. = 0.98 N

It is impractical to draw accurate force vector diagrams using this scale for the other three sets of data without a very large sheet of paper.

Tension = 11 NScale : 1 cm = 2 N

85oVertical comp.

= 0.98 N

75o

Tension = 3.8 N

Scale : 5.0 cm = 1 N

Vertical comp. = 0.98 N