An object hangs by means of two cords around two rods, as shown. The object is held in equilibrium by the forces F1 and F2.

Question 1

An object hangs by means of two cords around two rods, as shown.

The object is held in equilibrium by the forces F1 and F2. The object weighs 10 N. There is negligible friction between the rods and cords. Angle θ is 90°.

Which row of the table gives an angle θ of 90°?

F1 / N               F2 / N

A          4.0                   6.0

B          6.0                   4.0

C         6.0                   8.0

D         8.0                   6.0

Reference: Past Exam Paper – March 2017 Paper 12 Q14

Solution:

Answer: C.

The 2 forces F₁ and F₂ will also be along the cords.

Since the object is held in equilibrium, the resultant of the forces F₁ and F₂ should be equal to the weight of the object (= 10N).

The resultant of 3 vectors can be obtained by the triangle method.

From the question, we know that the angle between F₁ and F₂ is 90°. So, the triangle formed is actually a right-angled triangle. Also, the weight of the object is taken as the hypotenuse (since the other 2 forces formed the right angle).

From Pythagoras’ theorem,

F₁² + F₂² = 10²

It can be seen that both choices C and D apply to this equation.

But, now, let’s say that both forces were of the same magnitude, the object would have been midway between the 2 rods. But since the object is closer to the rod on the right, the force should be greater there.

So, F₂ > F₁.