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PHYSICS 1L03 (115)
Reza Nejat (43)


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Reza Nejat

Phys 1L03 Tutorial session Set 7 Seventh series: Questions on Center of mass, and Torque Concept: 1. Three masses, 2.0 kg, 3.0 kg, and 6.0 kg, are located at points (3.0, 0), (6.0, 0), and (-4.0, 0), respectively, in meters from the origin. Where is the center of mass of this system? 2. A dumbbell, Figure below, has a connecting bar of negligible mass. Find the location of the center of mass a. if m 1nd m ar2 each 5.0 kg and b. if m1 is.0 kg and m i2 10.0 kg. 3. A water molecule consists of an oxygen atom and two hydrogen atoms. Oxygen has a mass of 16 atomic units (u) and each hydrogen has a mass of 1 u. The hydrogen atoms are each at an average distance of 96 pm ( 96 x 10 -12 m) from the oxygen atom, and are separated from one another by an angle of 104.5 . Find the center of mass of a water molecule. 4. Two children are balanced on a see-saw of negligible mass. (This assumption is made to keep the example simple.) The first child, sitting on left side of the pivot, has a mass of 26.0 kg and sits 1.60 m from the pivot. The second child, sitting on right side of pivot, has a mass of 32.0 kg and 1.3 m from the pivot. Calculate the position of center of mass of the two children: a. from the first child b. from the pivot point. 5. Three balls A, B, and C, with masses of 3 kg, 1 kg, and 1 kg, respectively, are connected by massless rods. The balls are located as in Figure below. What are the coordinates of the center of mass? 6. Alley club-ax consists of a symmetrical 8 kg stone attached to the end of a uniform 2.5 kg stick that is 98 cm long. The dimensions of the club-ax are shown in Figure blow. How far is the center of mass from the handle end of the club-ax? Phys 1L03 Tutorial session Set 7 Seventh series: Questions on Torque, and Levers Concept: Torque : is a tendency of a force to change the rotational motion. Torque [τ] = (Force applied [F]) x (lever arm [r ⊥) Where: the lever arm, r⊥,is defined as the perpendicular distance from the axis of rotation to the line of action of the force. Or: τ = F r sinθ τ = F r ⊥ τ = F r ⊥ Where: r ⊥is the lever arm and ⊥ isthe force component perpendicular to the line of action of the force. Lever: is a rigid bar (e.g. Bone) tha
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