Question

A (c) Figure 1 shown below is a diagram of a non-uniform wooden plank, AB, which is 2.0 m long and weighs 1000 N. The plank is supported from a ceiling by two vertical springs, P and Q. The plank is attached at a distance of 0.5 m from each end. C is the centre of gravity as shown in Figure 1. P 0.5 m elek C 0.5 m W = 1000 N Figure 1. Diagram of a non-uniform wooden plank supported by two springs, P and Q. B When the plank is horizontal, the tension in Spring P is 600 N. a. Draw a force diagram showing all the information given in the question and Figure 1. (3 marks) b. Calculate the tension in Spring Q. Show ALL working. (2 marks) c. By taking moments about A, determine the horizontal distance from P to C. (5 marks) d. State why the centre of gravity is located closer to the point P than the point Q. (1 mark)​

Answer 1

A.) Draw a force diagram showing all the information given in the question and Figure 1:

[Force Diagram]

B.) Calculate the tension in Spring Q. Show ALL working:

Using Newton's Second Law of Motion, the sum of forces in the horizontal direction must equal 0. Therefore, TQ + TP - W = 0

Substituting the values given, TQ + 600N - 1000N = 0

Solving for TQ, TQ = 400N

C.) By taking moments about A, determine the horizontal distance from P to C:

Taking moments about A, we get: TQ x (2-x) - TP x x = 0

Substituting the values given, 400N x (2-x) - 600N x x = 0

Solving for x, x = 2m

Therefore, the horizontal distance from P to C is 2m.

D.) State why the centre of gravity is located closer to the point P than the point Q:

The centre of gravity is located closer to the point P than the point Q because the tension in spring P is greater than the tension in spring Q. The greater the tension in the spring, the more the board will be pulled in that direction, leading to a gravitational centre closer to the higher tension spring.