A rehabilitation patient is doing arm curl exercises by lifting a 90 N dumbbell (W), as shown, to strengthen their biceps muscle. The dumbbell is located 33 cm from the axis of rotation of the elbow joint. The arm is flexed as shown. The biceps muscle inserts 3 cm from the axis of rotation of the elbow joint and is oriented at an angle of 50° with respect to the arm. The motion is performed slowly enough that we can assume (quasi) static equilibrium. a) Determine the magnitude of the vertical joint reaction force Ry (shown) that the humerus exerts on the radius at the elbow joint. ) An equal and opposite compressive force then acts on the humerus. If we assume the humerus is a circular hollow cylinder with inner and outer radii of r;= 18 mm and ro. = 23 mm respectively, determine the resultant stress in the humerus. ) If the elastic modulus of bone is 15 GPa, determine the resultant strain in the humerus. d) If their humerus is initially 33 cm long, how much does it change in length (All go o rosult of this compressive lood2 Rx Ry [115 3cm FB 30 cm W = 90 N

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A rehabilitation patient is doing arm curl exercises by lifting a 90
N dumbbell (W), as shown, to strengthen their biceps muscle.
The dumbbell is located 33 cm from the axis of rotation of the
elbow joint. The arm is flexed as shown. The biceps muscle
inserts 3 cm from the axis of rotation of the elbow joint and is
oriented at an angle of 50° with respect to the arm. The motion
is performed slowly enough that we can assume (quasi) static
equilibrium.
a) Determine the magnitude of the vertical joint reaction force
Ry (shown) that the humerus exerts on the radius at the
elbow joint.
b) An equal and opposite compressive force then acts on the
humerus. If we assume the humerus is a circular hollow
cylinder with inner and outer radii of r;= 18 mm and ro. = 23
mm respectively, determine the resultant stress in the
humerus.
c) If the elastic modulus of bone is 15 GPa, determine the
resultant strain in the humerus.
d) If their humerus is initially 33 cm long, how much does it
change in length (Al) as a result of this compressive load?
Does your answer seem reasonable? Why or why not?
Rx
Ry
[115
50%
3 cm.
FB
30 cm
W = 90 N
Transcribed Image Text:A rehabilitation patient is doing arm curl exercises by lifting a 90 N dumbbell (W), as shown, to strengthen their biceps muscle. The dumbbell is located 33 cm from the axis of rotation of the elbow joint. The arm is flexed as shown. The biceps muscle inserts 3 cm from the axis of rotation of the elbow joint and is oriented at an angle of 50° with respect to the arm. The motion is performed slowly enough that we can assume (quasi) static equilibrium. a) Determine the magnitude of the vertical joint reaction force Ry (shown) that the humerus exerts on the radius at the elbow joint. b) An equal and opposite compressive force then acts on the humerus. If we assume the humerus is a circular hollow cylinder with inner and outer radii of r;= 18 mm and ro. = 23 mm respectively, determine the resultant stress in the humerus. c) If the elastic modulus of bone is 15 GPa, determine the resultant strain in the humerus. d) If their humerus is initially 33 cm long, how much does it change in length (Al) as a result of this compressive load? Does your answer seem reasonable? Why or why not? Rx Ry [115 50% 3 cm. FB 30 cm W = 90 N
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