Chapter No 4 Turning effect of forces

Transcription

1 1 Chapter No 4 Turning effect of forces Parallel forces: if a number of forces act on a body such that their points of action are different but direction of forces is parallel to each other is called parallel forces. Parallel forces are two types 1. Like parallel forces: Those parallel forces which have same direction are called like parallel forces 2. Unlike parallel forces: Those parallel forces which have opposite direction are called unlike parallel forces Addition of forces: The process by which two or more forces are added is called addition of forces. The vector sum of the forces on a body is important because it determines the direction and behavior of the force. The rules used for addition of forces are given below In case of like parallel forces, add magnitude of the forces In case of unlike parallel forces, subtract magnitude of the forces In case of non parallel forces, special method is used called heat to tail rule.

2 2 Head to tail rule: The method of adding forces in such way that the head of the first is joint with the tail of the second and the head of the second is joint with the tail of the third and so on is called Head to tail rule. The resultant force is obtained by joining the tail of first to head of last force. Example. Let cyclist is moving toward north at force F1 and wind is blowing toward east at force F2. The net force on a cyclist according to head to tail rule will be F Resolution of force: The process which is used to split a single force into its component is called resolution of force. The components of force which are perpendicular (making 90 angle) to each other is called rectangular components of the force. Explanation: consider force F which is making angle with x-axis. When the force F is resolved into its rectangular components it will give Fx and Fy

3 3 Magnitude of horizontal and vertical components Magnitude and direction of resultant force. As F 2 = Fx 2 + Fy 2 by Pythagorean Theorem Torque or moment of force: Definition: The tendency of a force to produce rotation in a body about an axis is called torque or momentum of force. OR The turning effect of force on a body is called torque Mathematically Torque produced in a body is equal to the product of force and moment arm. Torque = force X moment arm

4 4 Factors affecting torque: Torque depends upon two factors: 1. Magnitude of force (F): Greater the magnitude of force greater will be torque 2. Magnitude of moment arm (r) : The perpendicular distance between the axis of rotation and the line of the action of force is called the moment arm of the force. The longer the moment arm of the force greater will be torque. Unit of Torque: Torque is a vector quantity and unit is Newton metre or Nm. Example: When we rotate the door, torque is produced. Greater the force and longer the moment arm greater will be turning effect of door. Types of Torque: there are two types of torque 1. Anticlockwise torque: If a body rotates about its axis in anti clockwise direction then it is called anticlockwise torque and taken as positive. 2. Clockwise torque: If the body rotates in the clockwise direction then it is called clockwise torque and taken as negative. Principle of moment: According to this principle When a body is in equilibrium, the sum of clockwise moments must be equal to the sum of anticlockwise moments For example, when the SEASAW is balanced at a pivot then clockwise torque is equal to the anticlock wise torque. Centre of mass: The point in a body at which mass is equally distributed in all direction is called centre of mass. It is denoted by c.m The force applied at this point will only produce linear acceleration.

5 5 Example. The centre of mass of uniform wooden rod is its centre (mid point) Couple: The two parallel forces which are equal in magnitude but opposite in direction and do not act along the same line of action is called couple. The couple produces the rotational motion. The resultant force of a couple is zero For example, we apply forces with our two hands to turn the steering wheel of the vehicle as a couple. When both hands apply the forces which are equal in magnitude but opposite in direction wheel rotates due to couple. Statics Static is the branch of mechanics which deals with the study of bodies at rest under a number of forces. For example, the equilibrium, conditions of equilibrium, types of equilibrium, torque etc. Equilibrium Definition: A body is said to be in equilibrium if it is at rest or moving with uniform velocity. OR If the linear and angular acceleration of a body are zero, the body is said to be in equilibrium.

6 6 Explanation: when two or more forces act on a body such that their resultant or combining effect on the body is zero and the body retains its state of rest or of uniform motion then the body is said to be in equilibrium. Example A book lies on the table, suspended bodies, all stationary bodies, jump by using parachute. Types of equilibrium With respect to the state of a body, equilibrium may be divided into two categories: 1. Static equilibrium If the combined effect of all the forces acting on a body is zero and the body is in the state of rest then its equilibrium is termed as static equilibrium. For example: All stationary bodies 2. Dynamic equilibrium When a body is in state of uniform motion and the resultant of all forces acting upon it is zero then it is said to be in dynamic equilibrium. For example: Jump by using parachute. Conditions of equilibrium There are two conditions of equilibrium given below. First condition of equilibrium Definition: A body will be in equilibrium if the sum of all the forces acting on the body is zero

7 7 Mathematically: where F= Fx + Fy +Fz Explanation: According to first condition of equilibrium, to maintain transitional equilibrium in a body the sum of all the forces acting on the body is equal to zero. In other words we can say that to maintain equilibrium the sum of all the forces acting along X-axis is equal to the sum of all forces acting along Y-axis. For example, stationary person Second condition of equilibrium Definition: A body will be in equilibrium if the sum of all the torques acting on the body is zero Mathematically: where = sum of clockwise torque + sum of anticlockwise torque

8 8 Explanation: According to second condition of equilibrium a body will be in rotational equilibrium when the vector sum of all the torques acting on it is zero. When the sum of all torques on the body is zero there will be no change in the rotational motion of the body and a body is said to be in rotational equilibrium. Stability: A body in equilibrium is called stability of the body. Stability of the body depends upon the position of the centre of the gravity of the body. There are three states of equilibrium on the basis of stability. 1. Stable equilibrium When the center of gravity of a body lies below point of suspension or support, the body is said to be in stable equilibrium. For example a book lying on a table is in stable equilibrium. In stable equilibrium the body will come back to its original position when slightly disturbed. Reason of stability When the book is lifted its center of gravity is raised. The line of action of weight passes through the base of the book. A torque due to weight of the book brings it back to the original position. 2. Unstable equilibrium

9 9 When the center of gravity of a body lies above the point of suspension or support, the body is said to be in unstable equilibrium. In unstable equilibrium the body will not come back to its original position when slightly disturbed. Example pencil standing on its point or a stick in vertically standing position. Reason of instability when the pencil is slightly disturbed its center of gravity is lowered. The line of action of its weight lies outside the base of pencil. The torque due to weight of the pencil toppled it down. 3. Neutral equilibrium When the center of gravity of a body lies at the point of suspension or support, the body is said to be in neutral equilibrium. Example: rolling ball. Reason of neutral equilibrium If the ball is rolled, its center of gravity is neither raised nor lowered. This means that its center of gravity is at the same height as before.

10 10 Exercise Objectives 1. D 2. B 3. C 4. D 5. C 6. B 7. A 8. B 9. A 10. A Conceptual questions. 1. In which of the following case or cases, there is no horizontal force on the suitcase and why In case (a), there is no horizontal component because the force acting on the suitcase is perpendicular. So when the force is resolved into its component it will have only Fy components no Fx as original force lie perpendicular. 2. In which case the x and y components are equal to one another. Explain. SUPERIOR LALAZAR PUBLIC SCHOOL AND COLLEGE THANA Ph

11 11 In case B, the force makes angle of 45 so horizontal and vertical components must have same value. Fx = FCos = 100 cos 45 = 100x = 70.7N Fy = FSin = 100 sin 45 = 100x = 70.7N 3. Why is it more difficult to lean backwards? Explain Reason: It is more difficult to lean backwards because the centre of gravity of the body lower and unstable equilibrium establishes and difficult to come back to original position. 4. Explain why door handles are not put near the hinges? Reason: Door handles are not put near to hinges because moment of arm will be short and turning effects or torque directly depend upon moment of arm. Therefore it will be too hard to open or rotate the door when handles are put near the hinges. To minimize force door handles are not put near to hinges. 5. Why a helicopter does have a second rotor on its tail? Reason: The main rotors of the helicopter produce torque which could disturb equilibrium of helicopter or cause the helicopter to rotate. In order to keep the helicopter at equilibrium or in straight motion the sum of all torques must be zero. Therefore a second rotor is installed on helicopter SUPERIOR LALAZAR PUBLIC SCHOOL AND COLLEGE THANA Ph

12 12 tail to cancel the effect of anticlock wise rotation. main rotor or to balance clockwise rotation to 6. Why is it better to use a long spanner rather a short one to tight a nut on a bolt? Reason. We know the equation of torque From above equation it is clear that it is better to use a long spanner rather a short one to tight a nut on a bolt because moment of arm increases which increase torques and reduce the required force. 7. Which of these glasses in the most stable explain. From figure, the glass C is more stable because if we disturb their equilibrium by applying small force the glass c will easily come back to its original position as compared to glasses A and B. 8. A girl is seated safely and steadily in a canoe when she tries to stand up the canoe capsizes explain. Reason: A girl is seated safely and steadily in a canoe because the centre of mass is uniformly distribute so centre of gravity in this case SUPERIOR LALAZAR PUBLIC SCHOOL AND COLLEGE THANA Ph

13 13 cannot be changed easily but when she tries to stand up the centre of gravity changes and unstable equilibrium establishes due to which hard to keep in standing position. 9. How you determine the centre of irregular shape body? Reason: to find the centre of mass of irregular shaped body, make three holes at different position. Suspend the body from theses holes and draw lines. The intersection of these lines gives centre of gravity of irregular shaped body. 10. The gravitational force acting on a satellite is always directed towards the centre of the earth. Does this force exert torques on satellite? Reason. The gravitational force acting on a satellite is always directed towards the centre of the earth but it does not exert torque on satellite because for central force r is zero and hence the torque is zero. In this case force is applied on axis of rotation (centre of earth). Additionally as torque = rxf= rfsin where = 180 so torque = 0 because sin180= 0.

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