# Theme 2 - PHYSICS UNIT 2 Forces and Moments. A force is a push or a pull. This means that whenever we push or pull something, we are doing a force.

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1 Forces A force is a push or a pull. This means that whenever we push or pull something, we are doing a force. Forces are measured in Newtons (N) after the great physicist Sir Isaac Newton. The instrument which we use to measure force is the Newton balance. There are many things that a force can do but generally we may say that a force can: Cause movement from rest and increase the speed of moving objects Stop movement and decrease speed Change the direction of a moving object May stretch, compress, twist and turn objects. We can draw a force using an arrow. We use an arrow because this shows the size and the direction of the force. T2010 Page 1

2 Main Types of Forces 1. Weight Every object on earth is attracted towards the ground by a gravitational force (or force of gravity). The weight of an object is the force with which the gravity pulls on the object. It is measured in Newtons. The more mass an object has the greater is the pull of gravity on it. In fact, the relationship between an object s mass and its weight is given by the equation: Weight = mass x gravity W = m x g Where m is the mass of the object in kg and, g is the force per unit mass exerted by earth. The value of gravity on Earth = 10 N/kg The value of gravity on the moon = 1.67 N/kg 2. Contact force This is the push produced when two objects are in contact. There are two types: a) Reaction force - If a heavy load is placed on a table, we may be correct in saying that the load is pushing down on the table. The table reacts to this push by exerting and upward push on the load. The pushing force of the table on the load is known as a reaction force. T2010 Page 2

3 b) Friction - These are forces which resist motion. The forces between the surfaces of two objects which act parallel to the surfaces and prevent them slipping or sliding are called friction ADVANTAGE - Friction is useful when we apply the brakes of the car. DISADVANTAGE - Friction works against us when we push an object. Reducing friction: Method How they help to reduce friction 1. Polishing Make surface of object smoother. This is why it is more difficult to walk on ice than on tarmac. 2. Lubrification Separate surfaces by means of oil. This is done in car engines to reduce friction in the pistons. 3. Air Cushion Separate surfaces with an air cushion. This is how an air-hockey machine works. 4. Rolling Roll object instead of sliding it. You will have less area of contact and the friction will be less. 5. Streamline Shape of object reduces friction with air. This is why sports cars have aero-dynamics. 3. Tension A stretched rope or spring pulls at both of its ends as it tries to reduce its length back to normal.the pull of a string is called tension. T2010 Page 3

4 4. Upthrust force All objects no matter how heavy they all experience an upward force when immersed in a liquid. For example, lifting a stone in water is easier than lifting it in air. This is because the water is helping you lifting the stone. 5. Drag forces (Air Resistance) When a body moves through a fluid (liquid or gas) a drag force acts which opposes the body s motion. If the body is moving in air, this drag force is called air resistance. 6. Magnetic forces These are forces between magnetic materials. Two magnets with unlike poles North-South attract each other with a magnetic force. Like poles North-North or South- South repel each other. 7. Electric forces When certain materials are rubbed they acquire an electric charge. For example a Perspex rod when rubbed with a cloth it becomes charged and pieces of paper are attracted towards it. The force between the charged bodies is known as electrostatic forces. Drawing Force Diagrams When drawing force diagrams you should keep in mind the following points: Draw all objects as rectangles. Draw forces as arrows coming in or out of the sides of the rectangle. Write the size of the force near the arrow. T2010 Page 4

5 Balanced and Unbalanced Forces When two forces acting on an object are equal in size but act in opposite directions, we say that they are balanced forces. an object that is not moving stays still. an object that is moving continues to move at the same speed and in the same direction. If the forces on an object are unbalanced this is what happens: an object that is not moving starts to move an object that is moving changes speed or direction Resultant forces The size of the overall force acting on an object is called the resultant force. If the forces are balanced, this is zero. In the example above, the resultant force is the difference between the two forces, which is = 40N. When the forces are acting in the same direction they add up and when they are acting in opposite direction they subtract. T2010 Page 5

6 Vectors and Scalars: A vector quantity is a quantity that is specified by its size and direction (ex: the velocity of a car). A scalar quantity is a quantity that is specified by size only (ex: mass). Mass does not have any direction. Scalars Length, Area, Volume, Distance Mass, Density, Pressure, Time Speed Temperature, Energy Work, Power Vectors Direction, Displacement Acceleration, Momentum Velocity Weight Force Moments: The turning effect of a force is called the moment of the force. It is calculated by: Moment of Force = Force x Perpendicular Distance Note that the distance is always the shortest perpendicular ) distance between the force and the pivot. Moments are measured in newton-metres (written as Nm). Here is an example of balanced moments. 10N at 2m from the pivot is balancing 20N at 1m from the pivot. The objects create moments of 20Nm that are equal and opposite, so the see-saw is balanced. T2010 Page 6

7 Using moments A see-saw will balance if the moments on each side of the pivot are equal. This is why you might have to adjust your position on a see-saw if you are a different weight from the person on the other end. If a nut is difficult to undo with a short spanner, a longer spanner will help. This is because there will be a bigger moment on the nut, when the same force is applied further from the pivot. Using the same principle you can increase the moment applied by a lever or a crowbar, and this can help you move heavy objects more easily. 2m 3m 5m 4N 2N 2N Moment = Force x distance Moment = Force x distance Moment = Force x distance = 4 x 2 = 8Nm = 2 x 3 = 6Nm = 2 x 5 = 10Nm Clockwise and Anticlockwise Moments: The diagrams below show two cans lying on different sides of the pivot of a see-saw. Force 1 F1 Force 2 F2 In each of the two cases the see-saw will turn. A force can produce either a clockwise or an anticlockwise moment, depending on which side of the pivot the force is applied. In the above diagram: F1 will produce an anticlockwise moment. F2 will produce a clockwise moment. T2010 Page 7

8 When the clockwise moment = anticlockwise moment, the ruler will remain in equilibrium (will be balanced). This is known as the law of moments. the sum of the forces acting on it in one direction must equal the sum of the forces acting on it in the opposite direction the sum of moments about any point on the body must equal the sum of the anti-clockwise moments We can apply these two conditions to any object which is in equilibrium and use the equations to find any unknown forces. 0.3m 0.15m 100g 200g First we need to change the mass from grams to kilograms. Then use weight = mass x gravity to find the force. Clockwise moment = F x d = 1 x 0.3 = 0.3Nm Anticlockwise moment = F x d = 2 x 0.15 = 0.3Nm Centre of Gravity Every object is made up of tiny particles called atoms. Although the force of gravity pulls down on every little atom, the weight of the object seems to act at its centre. This point, where the object is in equilibrium (i.e. in balance), is called the centre of gravity. (c.o.g.) or the centre of mass. The centre of gravity is the point through which the whole weight of the object seems to act. T2010 Page 8

9 Stability A body is in stable equilibrium if when slightly displaced and then released it returns to its previous position. The ball even if tilted through a large angle and then released, it will return to its original position. Its centre of gravity rises when displaced but it falls back because its weight has a moment about the point of contact. A body is in unstable equilibrium if it moves farther away from its previous position when slightly displaced. The ball behaves in this way. Its centre of gravity falls when slightly displaced. A body is in neutral equilibrium if when displaced its centre of gravity does not rise or fall. Toppling The position of the centre of gravity effects whether or not a body topples over easily. This is important in the design of such things as high vehicles (which tend to overturn when going round a corner), racing cars, reading lamps and even teacups, drinks containers, double decker buses,loading of ships. A body topples when the vertical line through its centre of gravity falls outside its base, otherwise it remains stable. T2010 Page 9

10 Finding the c.o.g For a regular shaped object, the Centre of Gravity is found at the middle of that object. If we balance the object at that point, there will be a zero turning effect. If the object has an irregular shape, we can find its Centre of Gravity using the plumb line method. Three holes are drilled around the edges of the lamina. The lamina is hanged from one of its holes on a pin clamped on a retort stand and suspended from a pivot. A plumbline is attached to the pivot and its position marked. This is repeated for the other two holes and where the three lines meet, there is the centre of gravity of the lamina. Can you explain why it is easier to carry a ladder from the middle than from its ends. It is easier to carry the ladder from the middle because in this case the pivot is exactly on the centre of gravity of the ladder, and so the ladder will be balanced. Hooke s Law If a spring is fixed from one end and a load hung on the other end, the spring s length would increase. The increase in length is known as the extension Experiment shows that for every 1 Newton load that is placed on the spring, the spring would extend by the same amount. T2010 Page 10

11 Hooke s Law states that: The extension is directly proportional to the load applied on the spring provided that the elastic limit is not exceeded. However, after a certain weight the extension will no longer be proportional to the force and the spring will become permanently deformed, that is, the spring will no longer return to its original length. In such a case we say that we have exceeded the elastic limit. When a spring is loaded with weights, the extension produced in the spring increases when the weight (force applied) is increased. The extension of the spring is found by subtracting the original length from the new length. For the first few weights we can notice that the force and the extension are proportional to each other. This means that if the force is doubled, the extension of the spring will double and so on. The straight line on the graph is the region where Hooke s law is obeyed. The spring is deformed when on removing weights from the spring, it does not return to its original length. The spring will be permanently extended. T2010 Page 11

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