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.

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

The resultant tension, R = W = 42.415 N

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 = +

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 = + = 42.415.

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