Selected Topics in Physics for Medical Sciences Students

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Selected Topics in Physics for Medical Sciences Students Unit 2 Static and Equilibrium Lecture

Selected Topics in Physics for Medical Sciences Students Unit 2 Static and Equilibrium Lecture 6 Examples Physics Academy www. physicsacademy. org Dr. Hazem Falah Sakeek Al-Azhar University - Gaza

Contents Statics & Equilibrium • Introduction • Torques • Couples • Equilibrium of Rigid

Contents Statics & Equilibrium • Introduction • Torques • Couples • Equilibrium of Rigid Bodies • Selected Topics • Problems 2 Dr. Hazem F. Sakeek www. physicsacademy. org

Exercise 1 A 30 kg pile of rocks is balanced by a 5. 0

Exercise 1 A 30 kg pile of rocks is balanced by a 5. 0 kg block of wood on a scale, as shown below. The rocks are 0. 30 m from the pivot point. How far, to the other side of the pivot point, must the block of wood be placed (ignore the mass of the scale)? 0. 30 m d ØAnswer: d=1. 8 m 3 Dr. Hazem F. Sakeek www. physicsacademy. org

Example 1 Given M = 120 kg. Neglect the mass of the beam. a)

Example 1 Given M = 120 kg. Neglect the mass of the beam. a) Find the tension in the cable b) What is the force between the beam and the wall 4 Dr. Hazem F. Sakeek www. physicsacademy. org

Solution a) Given: M = 120 kg, L = 10 m, x = 7

Solution a) Given: M = 120 kg, L = 10 m, x = 7 m Find: T Axis Solve for T = 824 N 5 Dr. Hazem F. Sakeek www. physicsacademy. org

Solution b) Given: M = 120 kg, L = 10 m, x = 7

Solution b) Given: M = 120 kg, L = 10 m, x = 7 m, T = 824 N Find f f Solve for f = 353 N 6 Dr. Hazem F. Sakeek www. physicsacademy. org

Exercise 2 A seesaw consisting of a uniform board of mass M and length

Exercise 2 A seesaw consisting of a uniform board of mass M and length l supports a father and daughter with masses mf and md, respectively, as shown in Figure. The support (called the fulcrum) is under the center of gravity of the board, the father is a distance d from the center, and the daughter is a distance l/2 from the center. (A) Determine the magnitude of the upward force n exerted by the support on the board. (B) Determine where the father should sit to balance the system. 7 Dr. Hazem F. Sakeek www. physicsacademy. org

 Because the system in equilibrium then the net force = zero 8 Dr.

Because the system in equilibrium then the net force = zero 8 Dr. Hazem F. Sakeek www. physicsacademy. org

 Applying the secondition of the equilibrium 9 Dr. Hazem F. Sakeek www. physicsacademy.

Applying the secondition of the equilibrium 9 Dr. Hazem F. Sakeek www. physicsacademy. org

Exercise 3 A person holds a 50. 0 -N sphere in his hand. The

Exercise 3 A person holds a 50. 0 -N sphere in his hand. The forearm is horizontal, as shown in Figure. The biceps muscle is attached 3. 00 cm from the joint, and the sphere is 35. 0 cm from the joint. Find the upward force exerted by the biceps on the forearm and the downward force exerted by the upper arm on the forearm and acting at the joint. Neglect the weight of the forearm. F=583 N R=533 N 10 Dr. Hazem F. Sakeek www. physicsacademy. org

 Solution: We simplify the situation by modeling the forearm as shown in the

Solution: We simplify the situation by modeling the forearm as shown in the figure, where F is the upward force exerted by the biceps and R is the downward force exerted by the upper arm at the joint. From the first condition of equilibrium we have, From the secondition of equilibrium about point O we have, 11 Dr. Hazem F. Sakeek www. physicsacademy. org

Exercise 4 A uniform horizontal beam with a length of 8. 00 m and

Exercise 4 A uniform horizontal beam with a length of 8. 00 m and a weight of 200 N is attached to a wall by a pin connection. Its far end is supported by a cable that makes an angle of 53. 0° with the beam. If a 600 -N person stands 2. 00 m from the wall, find the tension in the cable as well as the magnitude and direction of the force exerted by the wall on the beam. T=313 N R=580 N Θ=71. 1 o 12 Dr. Hazem F. Sakeek www. physicsacademy. org

 Applying the first condition of the equilibrium From the secondition of equilibrium about

Applying the first condition of the equilibrium From the secondition of equilibrium about point O we have, 13 Dr. Hazem F. Sakeek www. physicsacademy. org

Exercise 5 Suppose that you placed a 10 m ladder (which weights 100 N)

Exercise 5 Suppose that you placed a 10 m ladder (which weights 100 N) against the wall at the angle of 30°. What are the forces acting on it and when would it be in equilibrium? 30 14 Dr. Hazem F. Sakeek www. physicsacademy. org

Solution: Given: weights: w 1= 100 N length: l=10 m angle: a=30° St =

Solution: Given: weights: w 1= 100 N length: l=10 m angle: a=30° St = 0 mg a 1. Draw all applicable forces 2. Choose axis of rotation at bottom corner (t of f and n are 0!) Find: Torques: f= ? n=? P=? Forces: ü ü Note: f = ms n, so 15 Dr. Hazem F. Sakeek www. physicsacademy. org