Download Biomechanics Sheet 1

Biomechanics Sheet 1
1. When a person’s head is tilted forward the posterior neck muscles must contract
to maintain equilibrium. What force must these muscles exert to support the head
in this forward position as shown in figure? What is the joint reaction force
(magnitude and direction) at the atlanto-occipital joint in this position? When the
head is in the upright position, the muscle force is zero and the joint reaction force
is 6.3 kg.
2. For the two positions of the upper limb shown below, compare the deltoid
muscle force D and the shoulder joint reaction force. Assume the deltoid is the
only muscle which acts to keep the humerus in the horizontal position. The deltoid
makes an angle of 15o with the horizontal. W1 = 1.4 kg, W2 = 1.1 kg, W3 = 0.5
kg, d1 = 10 cm, d2 = 13 cm, d3 = 25 cm, d4 = 22 cm, d5 = 25 cm.
3. A patient is seated and extends his knee joint to exercise the quadriceps muscle.
The figure shows the knee at 90o flexion. For the two positions of 90o flexion and
full extension, compare the following:
a. Quadriceps muscle force
b. Knee joint reaction force magnitude and direction.
Assume that the line of action of the quadriceps muscle force Q makes an angle of
25o with the axis of the tibia in all positions.
4. Figure 4-a shows an outstretched arm with a mass of 4.2 kg. The arm is 56 cm
long, and its center of gravity is 21 cm from the shoulder. The hand at the end of
the arm holds a 6.0-kg mass.
(a) What is the torque about the shoulder due to the weights of the arm and the
6.0-kg mass?
(b) If the arm is held in equilibrium by the deltoid muscle, whose force on the arm
acts 5.0◦ below the horizontal at a point 18 cm from the shoulder joint (Fig. 4-b),
what is the force exerted by the muscle?
5. Figure 5 shows the foot and lower leg of a person standing on the ball of one
foot. Three forces act on the foot to maintain this equilibrium: the tension force T
in the Achilles tendon, contact force FC at the ankle joint, and the normal force N
of the ground that supports the person’s weight. The person’s mass is 70 kg, and
the force application points are as indicated in Fig.5. Find the magnitude of
(a)The tension in the Achilles tendon and
(b)The contact force at the ankle joint.
6. Determine the forces and moments exerted in hip (at points A and B) and knee
(at point K) joints respectively.
Femur: mf =20kg Tibia: mt =10kg
7. Based on the assumption that the air resistance is negligible. The driver illustrated
in figure 7 undergoes both translational and rotational, or general motion. The
overall translational motion of the driver can be analyzed by observing the trajectory
of the diver’s center of gravity which can be assumed to undergo a projectile
motion.
Consider a case in which a diver takes off from a diving board located at a height
h0 = 10 m above the water level and enters the water at a horizontal distance L = 5 m
from the end of the board. If the total time the diver remains in the air is t2 = 2.5 s,
calculate the speed and angle of takeoff of the diver’s center of gravity.