Question

8. Fig. 4.1 shows a heavy ball B of weight W suspended from a fixed beam by two ropes P and Q.

P and Q are both at an angle of 45° to the horizontal. The tensions in P and Q are each 30 N.
a. In the space below, draw a scale diagram to find the resultant of the tensions
in P and Q. Use a scale of 1.0cm to represent 5.0 N. Label the forces and show
their directions with arrows.

Answer 1

a. Please find attached the required scale diagram drawn to scale using Microsoft Word

The resultant tension, R = W = 42.415 N

Step-by-step explanation:

The given parameters are;

The angle P and Q makes with the horizontal = 45°

The tensions in the ropes P and Q = 30 N each

The weight of the heavy ball B suspended from the fixed beam by the ropes = W

The scale drawing is drawn using Microsoft Word

The required scale factor of the scale diagram, S.F. = 5.0 N/cm

Therefore, we have;

The length of the line representing the tensions P and Q = 30 N/(5.0 N/cm) = 6 cm

The length of the resultant vector, R =
`\underset{P}{\rightarrow}` +
`\underset{Q}{\rightarrow}`

By the parallelogram law of vector addition, by measurement, we have;

R = 8.483 cm

By conversion using the scale factor of the scale drawing, we have;

R = R × S.F. = 8.483 cm × 5.0 N/cm = 42.415 N

∴ The resultant in the tensions, R =
`\underset{P}{\rightarrow}` +
`\underset{Q}{\rightarrow}` = 42.415.