Question

Peter is trying to ignite the hotplate by turning the gas knob. Suppose thatthe minimum moment of couple about the center of the gas knob requiredto ignite the hotplate is 0.3 N m. Calculate the minimum force (F, and F2)that required to exert. Given that the diameter of gas knob is 5 cm.

Answer 1

the minimum force is 6 Newtons

Step-by-step explanation

A moment of a force, or a torque, is a measure of a force's tendency to cause a body to rotate. The moment depends on both the force, and on the position at which the force acts, it is given by the expression

`M=F\cdot d\text{ }`

where F is the exerted force and d is the distance

Step 1

then, let

`\begin{gathered} M=\text{0}.3\text{ Nm} \\ F=F \\ \text{distance}=\text{ 5 cm= }(5)/(100)m=0.05\text{ m} \\ \end{gathered}`

now, replace in the formula

`\begin{gathered} M=F\cdot d\text{ } \\ 0.3\text{ Nm=F}\cdot0.05\text{ m} \\ \text{divide both sides by 0.05 m} \\ \frac{0.3\text{ Nm}}{0.05\text{ m}}\text{=}\frac{\text{F}\cdot0.05\text{ m}}{0.05\text{ m}} \\ 6N=F \end{gathered}`

therefore, the minimum force is 6 Newtons

I hope this helps you