Question $2(8$ marks$)$

Consider a person pertorming strentitier coversises using a chubbeil. The forces acting on the Arm and a madel of the system are sthewn in the figere.

Point $O$ is the axis of ratation of the shouldier joint, $A$ is the point of attachment of the deltold muscle to the humerus, point $3$ is che cevere of graity of the arm, and point $C$ is the centre of gravity of the dumbibell, Points A and $B$ are at distances of $a=17cm$ and $b=33cm,$ from the shoulder respectively $($see top figure$).$ Fru is the force applied by the muscle and $R$ is the reaction force at the joint $0.$

The mass of the dumblell is $F{r}_0=6\mathrm{.}524kg.$ The magnitude of the muscle force is estimated to be $F_A=1051N,$ at an angle of $=18.$ The reaction force $R$ makes an angle with the horizontal of $={12}^2.$

a$)$ Determine the magnitude of the reaction force $R.$

$(2$ marks$)$

b$)$ Determine an equation in terms of the reaction force magnitude $(R)$ for the weight of the arm, W$.$

$(3$ marks$)$

c$)$ If $W=47N,$ find the length from the shoulder joint to the dumbbell, C $.$

$(3$ marks$)$