Question

In the diagram alongside, F₁ = F₂ acting on a wheel of radius 2.5 m produce a moment of couple of 100 Nm. The magnitude of each force acting on the wheel is:

Options

• 4.0 N

• 40.0 N

• 20.0 N

• 2.0 N

Answer 1

20.0 N

Explanation:

Radius of the wheel

\[ r = 2.5\ \mathrm{m} \]

Perpendicular distance between the two forces (Arm of the couple, d) = Diameter

\[ d = 2 \times r = 2 \times 2.5 = 5\ \mathrm{m} \]

Moment of couple

\[ = 100\ \mathrm{Nm} \]

Magnitude of each force

\[ = F_{1} = F_{2} = F \]

\[ \text{Moment of Couple} = \text{Force}\ (F) \times \text{Arm of the couple}\ (d) \]

\[ 100 = F \times 5 \]

\[ F = \frac{100}{5} \]

\[ F = 20\ \mathrm{N} \]