Question

Tendon forces Ta and Tb are exerted on the patella. The femur exerts force F on the patella. If the magnitude of Tb is 80 N, what are the magnitudes of Ta and F, if no motion is occurring at the joint? (Answer: Ta = 44.8 N, F = 86.1 N)

Answer 1

Complete question

The diagram for this question is shown on the first uploaded image

Answer:

`T_a   =  44.8 \  N` ,
`F =  86.03 \ N`

Step-by-step explanation:

From the question we are told that

The magnitude of
`T_b  =  80 N`

From the diagram we can see that

`Ta * sin (38) +  F *  sin (29) =   T_b *  cos  (30) \  \cdots (1)`

`Ta * sin (38) +  F *  sin (29) = 80 *  cos  (30) \  \cdots (1)`

`0.616 Ta +  0.485F  = 69.3 \  \cdots (1)`

=>
`T_a   = (69.3 - 0.485F)/(0.616)`

Also

`T_a  *  cos(38) + T_b *  sin (30)= F *  cos (29) \  \cdots  (2)`

=>
`T_a  *  cos(38) + 80*  sin (30)= F *  cos (29) \  \cdots  (2)`

=>
`0.788 T_a + 40 =  0.875 F \  \cdots  (2)`

=>
`0.788 [(69.3 - 0.485F)/(0.616)]+ 40 =  0.875 F`

=>
`88.65  -  0.6204 F + 40 =  0.875 F`

=>
`88.65  + 40 =  0.875 F+0.6204 F`

=>
`128.65  =  1.4954 F`

=>
`F =  86.03 \ N`

substituting this obtained value for F in the above equation

`T_a   = (69.3 - 0.485(86.03))/(0.616)`

`T_a   =  44.8 \  N`