Tutorial 1 - Drawing Free body diagrams and assessing forces applied PDF

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Drawing Free body diagrams and assessing forces applied ...

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BMEN20001 Biomechanical Physics & Computation Physics Tutorial Sheet 1

Lectures Weeks 1 & 2 Key Learning Outcomes • Apply principles of free body diagrams to sketch the forces acting on a system. • Evaluate the forces and moments in a mechanical system.

Question 1 As illustrated in Figure 1, consider two workers who are trying to move a block. Assume that both workers are applying equal magnitude forces of 200 N. One of the workers is pushing the block toward the north and the other worker is pushing it toward the east. Determine the magnitude and direction of the net force applied by the workers on the block.

Figure 1: Two workers moving a box.

Question 2 Consider the two forces, F1 and F2 , shown in Figure 2. Assume that these forces are applied on an object in the xy-plane. The first force has a magnitude F1 = 15 N and is applied in a direction that makes an angle α = 30◦ with the positive x-axis, and the second force has a magnitude F2 = 10 N and is applied in a direction that makes an angle β = 45◦ with the negative x-axis. (a) Calculate the scalar components of F1 and F2 along the x and y directions. (b) Express F1 and F2 in terms of their components. (c) Determine an expression for the resultant force vector, FR .

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(d) Calculate the magnitude of the resultant force vector. (e) Calculate the angle θ that FR makes with the positive y-axis.

Figure 2: A system of forces.

Question 3 Consider the total hip joint prosthesis shown in Figure 3. The geometric parameters of the prosthesis are such that l1 = 50 mm, l2 = 50 mm, θ1 = 45◦ , and θ2 = 90◦ . Assume that, when standing symmetrically on both feet, a joint reaction force of F = 400 N is acting at the femoral head due to the body weight of the patient. For the sake of illustration, consider three different lines of action for the applied force, which are shown in Figure 3. Determine the moments generated about points B and C on the prosthesis for all cases shown.

Figure 3: The pelvis and hip joint prosthesis.

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Question 4 Figure 4 illustrates a simplified version of a hamstring strength training system for rehabilitation and athlete training protocols. From a seated position, a patient or athlete flexes the lower leg against a set resistance provided through a cylindrical pad that is attached to a load. For the position illustrated, the lower leg makes an angle θ with the horizontal. Point O represents the knee joint, point A is the centre of gravity of the lower leg, W is the total weight of the lower leg, F is the magnitude of the force applied by the pad on the lower leg in a direction perpendicular to the long axis of the lower leg, a is the distance between points O and A, and b is the distance between point O and the line of action of F measured along the long axis of the lower leg. (a) Determine an expression for the net moment about O due to W and F . (b) If a = 20 cm, b = 40 cm, θ = 30◦ , W = 60 N, and F = 200 N, calculate the net moment about O .

Figure 4: Hamstring strength training system.

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Question 5 As illustrated in Figure 5, consider an athlete performing flexion/extension exercises of the lower arm to strengthen the biceps. The athlete is holding the weight of W1 = 150 N in his hand, and the weight of his lower arm is W2 = 20 N. As measured from the elbow joint at point O, the centre of gravity of the lower arm (point A) is located at a distance a = 7.5 cm and the centre of gravity of the weight held in the hand is located at a distance b = 32 cm. Determine the net moment generated about the elbow joint, when the lower arm is extended horizontally and when the long axis of the lower arm makes an angle f1 = 30◦ and f2 = 60◦ respectively with the horizontal.

Figure 5: An athlete performing flexion/extension exercises.

Question 6 Consider two blocks: block A, which weighs 5 N, is on the table. Block B, weighing 10 N, is on top of block A as shown in Figure 6. Analyse the forces that act on each block separately. Finally, determine the total contact force exerted by the two blocks on the table.

Figure 6: Two block setup.

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Question 7 Sketch a free body diagram for the hip joint when a person stands on one leg (shown in Figure 7).

Figure 7: (Left) Anatomy of the left leg and hip. (Right) Loads applied on the left leg.

Question 8 Investigate the nature of the knee joint and the patella muscle: draw a free body diagram of the lower leg to depict the joint reactions, muscle force, and weight of the lower leg. A sketch of the configuration of the bones and knee muscle is shown in Figure 8.

Figure 8: A sketch of the bones and knee muscle that constitute the lower leg.

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