Question

A woman carries a 12 kg box holding it in both armsa. How much force must be exerted on each of her arms to support the box?b. How will this force change if she holds the box with only one arm?

Answer 1

a)58.8 N

b)117.6 N

Explanation

Weight is a quantity representing the force exerted on a particle or object by an acceleration field , on earth we have weigth due to acceleratioi of gravity ,its value is

$g=\text{ 9.8}\frac{m}{s^2}$

caused by the presence of a massive second object,the earth

so, the weight is given as

$\begin{gathered} weigth=mg \\ where\text{ m is the mass} \end{gathered}$

Step 1

given

$mass=\text{ 12 kg}$

a) if she holds the box holding in both arms

the sum of force must equal zero, hence

$\begin{gathered} arm1+arm2-weigth=0 \\ arm1+amr2=weigth \end{gathered}$

so, the sum of the forces on both arms must equal tehh weigth of the box,

let's find the weigth of the box

$\begin{gathered} weigth=\text{ mg} \\ w=12\text{ kg*9.8}\frac{m}{s^2} \\ w=117.6\text{ Newtons} \end{gathered}$

so

$\begin{gathered} arm1+amr2=117.6\text{ N} \\ arm1=\text{ arm2, so} \\ 2(arm1)=117.6 \\ arm1=\frac{117.6N}{2} \\ arm=58.8\text{ N} \end{gathered}$

therefore, she must exerts a force of 58.8 Newtons on each arm

a)58.8 N

Step 2

now, if she holds the box with only one arm:

in this case, the weight of the box must be supported by only one arm, so

the force must be equal to the weigth of the box

$\begin{gathered} arm\text{ force= weigth} \\ arm\text{ force=mg} \\ armforce=12\text{ kg*9.8 }\frac{m}{s^2} \\ arm\text{ force= 117.6 N} \end{gathered}$

so

b)117.6 N

I hope this helps you