Discover Physics for GCE O Level Science Unit

Discover Physics for GCE ‘O’ Level Science Unit 3: Forces and Pressure

3. 1 Forces Learning Outcomes At the end of this section, you’ll be able to: • understand what a force is • describe some types of forces

3. 1 Forces What is a Force? • A Force is a push or pull that one object exerts on another. • It produces or tends to produce motion, and stops and tends to stop motion: Boy exerts a push on the boat Boy exerts a pull on the boat

3. 1 Forces What types of forces are there?

3. 1 Forces Quantifying Forces • The SI unit of force is newton (N). • A force of 1 N is roughly the amount of force the Earth’s gravity pulls on a 100 g mass.

3. 1 Forces Adding Forces • A force always acts in a particular direction. • Two or more forces may act on an object at the same time. • These forces can be added using vector diagrams.

3. 1 Forces Key Ideas • A force is a push or pull that one object exerts on another. It produces or tends to produce motion, and stops or tends to stop motion. • There are many types of forces, eg. Friction, weight, tension, magnetic force and electric force. • The SI unit force is the newton (N).

3. 1 Forces Test Yourself 3. 1 1. Name the types of forces in our daily lives. Answer: • Pushing or pulling force • Friction force • Repulsive/attractive force between poles of magnets • Gravitational force, weight • Contact force between you and the floor • Repulsive/attractive force between electric charges • Air Resistance

3. 2 Scalars and Vectors Learning Outcomes At the end of this section, you’ll be able to: • understand distinguish between scalar and vector quantities • add two vectors using a graphical method • solve problems involving three vectors acting on a static body

3. 2 Scalars and Vectors What are scalar and vector quantities? • Scalar quantities are physical quantities that have magnitude only. • Vector quantities are physical quantities that possess both magnitude and direction.

3. 2 Scalars and Vectors When referring to a scalar quantity, we only need to consider its magnitude. • Example: – The mass of an object is 2. 0 kg – The volume of the box is 5 m 3 – The distance traveled by the car is 800 m Scalar quantities are added by summing the magnitude • Example: A mass of 100 g added to 200 g gives a total of mass 300 g.

3. 2 Scalars and Vectors When referring to a vector quantity, we must consider both its magnitude and direction. Example: The car travels with a velocity of 20 ms-1 in the direction of 45 o North of East

3. 2 Scalars and Vectors How do we add vectors? • When adding vectors, both the magnitude and direction of the vectors must be considered. • Addition of two or more vectors together gives a single vector called the RESULTANT VECTOR

3. 2 Scalars and Vectors Addition of parallel vectors (Example 1) Resultant Force = 3 N + 5 N =8 N

3. 2 Scalars and Vectors Addition of Parallel Vectors (Example 2) Resultant Force = (-3 N) + 5 N =2 N

3. 2 Scalars and Vectors Addition of Parallel Vectors (Example 3) Resultant Force = (-3 N) + 3 N = 0 N The object is in a state of equilibrium i. e. it remains stationary or continues moving in a straight line.

3. 2 Scalars and Vectors Addition of non-parallel vectors using the parallelogram method In most cases, vectors such as forces act at an angle to each other, such as in the diagram below. We can use the parallelogram method (on the next slide) to find its resultant.

3. 2 Scalars and Vectors Parallelogram Method Addition of vectors: Using the parallelogram method

3. 2 Scalars and Vectors Tip-To-Tail Method Another method of adding non-parallel vectors is the tip-to-tail method. We can use the tip-to-tail method to find the resultant of the diagram below.

3. 2 Scalars and Vectors Tip-To-Tail Method Addition of vectors: Using the tip-to-tail method

3. 2 Scalars and Vectors Worked Example 3. 1 A weight W (6. 0 N) hangs on the end of a string, which is pulled sideways by a force F. The string makes an angle of 30 with the vertical, as show in the diagram. The string supports the weight by exerting a pull known as tension T of 7. 0 N. Determine the force F by using the (a) parallelogram method, (b) tip-to-tail method.

3. 2 Scalars and Vectors Solution to Worked Example 3. 1(a) Parallelogram Method: For the weight to be stationary, the resultant force must be zero. Therefore, force F must balance out the resultant of weight W and tension T. Hence, we will first find the resultant of W and T, then determine F. From the force parallelogram (as shown in the diagram), drawn with a scale of 1 cm: 2 N, the diagonal, which is the resultant of T and W, has a length of 1. 75 cm. In order to balance this resultant, F must be 1. 75 cm also. This means force F should be 3. 5 N.

3. 2 Scalars and Vectors Solution to Worked Example 3. 1(b) Tip-to-tail Method: Using an appropriate scale, e. g. 1 cm: 2 N, let W be the first force vector drawn, followed by T as the second vector. Force F is found by joining the end point of T to the start point of W to form a closed triangle. In doing so, the resultant force will be zero, and the system is in equilibrium (i. e. stationary in this case). By measuring the vector, F has a length of 1. 75 cm. Hence, force F = 3. 5 N. The answer is the same using the parallelogram method.

3. 2 Scalars and Vectors Key Ideas • A scalar quantity has magnitude only. • A vector quantity has magnitude and direction. • When there are two or more forces acting on an object, the resultant can be found by adding the forces together. > For parallel forces, the resultant force is found by taking one direction as positive and the opposite as negative, and then adding up the forces. > For non-parallel forces, the resultant force is found by adding the vectors using the parallelogram method or the tip-to-tail method.

3. 2 Scalars and Vectors Test Yourself 3. 2 1. A man can row a boat in still water at a speed of 1. 0 m s -1. The man sets out to row the boat in a river from A to B. The water in the river flows at 0. 5 m s-1 in the direction B to A. Find the velocity of the boat through the water. Answer: Since the velocity of water is acting opposite to that of the boat, the velocity of the boat through water, Vbw, is Vbw = Vb - Vw = 1. 0 - 0. 5 = 0. 5 m s-1

3. 2 Scalars and Vectors Test Yourself 3. 2 2. A lorry, which has been stuck in muddy ground, is being pulled by two jeeps. Each jeep exerts a force of 3000 N at an angle of 20 o to the horizontal in the direction shown. Find, using a scale diagram, the resultant force pulling the lorry forward. Answer: Using an appropriate scale diagram, the resultant force F = 5600 N 3000 N 20 o 3000 N 5600 N

3. 3 Forces and Motion Learning Outcomes In this section, you’ll be able to: • describe how a force changes the motion of a body • describe the effects of balanced and unbalanced forces on a body • identify forces acting on an object • state Newton’s three laws of motion

3. 3 Forces and Motion What is the effect of a force on motion? Forces can affect the movement of objects, as can be observed from our daily activities. • A force can cause a stationary object to start moving e. g. a football player kicking a football. • A force can cause a moving object to increase speed e. g. a person rollerblading gives a push to move even faster • A force can cause a moving object to decrease speed e. g. when cycling down a slope, a cyclist applies the brakes to slow down the bicycle. • A force can cause a moving object to changes its direction of motion e. g. during a game of badminton, a player intercepts and hits the shuttlecock to change its direction and motion.

3. 3 Forces and Motion • In each of the four examples given, there is a change in the motion of the object. • The velocity of an object changes with time i. e. there is acceleration. • A force can cause an object to accelerate or decelerate.

3. 3 Forces and Motion Forces and Zero Acceleration • Zero acceleration implies that object could be stationary or moving with constant velocity. • It does not mean there are no forces acting on it. A car at rest has zero acceleration. An ice skater gliding at constant velocity has zero acceleration.

3. 3 Forces and Motion Forces and Zero Acceleration For an object with zero acceleration, the different forces acting on it are balanced or add up to zero – i. e. the resultant or net force is zero.

3. 3 Forces and Motion Newton’s First Law of Motion Every object will continue in its state of rest or uniform motion in a straight line unless a resultant force acts on it to change its state. Forces acting on a book resting on a table show that F = W Book sliding along a frictionless surface at constant velocity.

3. 3 Forces and Motion Newton’s First Law of Motion Newton’s first Law of Motion is also know as the Law of Inertia. You will learn more about inertia in Unit 4: Mass, Weight and Density. Newton’s First Law is summarised in this simple flow chart.

3. 3 Forces and Motion Unbalanced Forces and Newton’s Second Law If the resultant force acting on an object is not zero, we say the forces are unbalanced. Forces cause the book to accelerate or decelerate.

3. 3 Forces and Motion Unbalanced Forces and Newton’s Second Law • Unbalanced forces causes an object to accelerate, decelerate or change direction. • The direction of acceleration is in the direction of the resultant force. Unbalanced forces and their relation to Newton’s Second Law

3. 3 Forces and Motion Unbalanced Forces and Newton’s Second Law of Motion: When a resultant force acts on an object of constant mass, the object will accelerate and move in the direction of the resultant force. The product of the mass and acceleration of the object is equal to the resultant force. F = ma where F = resultant force (in N) m = mass of object (in kg) a = acceleration of object (in m s-2)

3. 3 Forces and Motion Unbalanced forces and Newton’s Second Law The SI unit of force is newton (N). One newton (1 N) is defined as the force that will produce an acceleration of 1 m s-2 on a mass of 1 kg. If m = 1 kg and a = 1 m s-2, then using the equation F = ma = (1 kg)(1 m s-2) =1 N

3. 3 Forces and Motion Worked Example 3. 2 A boy pushes a box of mass 20 kg with a force of 50 N. What is the acceleration of the box? (Assume no friction. ) 50 N 20 kg Solution: Given that mass m = 20 kg and force F = 50 N From Newton’s Second Law, F = ma. Then, 50 F = = 2. 5 m s-2 a = m 20

3. 3 Forces and Motion Worked Example 3. 3 A car of mass 1000 kg accelerates from rest to 20 m s -1 in 5 s. Calculate the forward thrust of the car (assume no friction). Solution: Given mass m = 1000 kg, initial speed u = 0 m s-1, final speed v = 20 m s-1 and time t = 5 s From Newton’s Second Law, forward thrust F = ma where a = acceleration produced But a = 20 - 0 v-u = 4 m s-2 = t 5 F = ma = (1000)(4) = 4000 N

3. 3 Forces and Motion Weight is a force Weight is an ever-present force exerted on every object due to gravity. The acceleration of free fall ‘g’ due to Earth’s gravity is 10 m s-2. Weight = Force W= F F = ma F = mg W = mg

3. 3 Forces and Motion Newton’s Third Law (Optional) Newton’s Third Law of Motion states that: For every action, there is an equal and opposite reaction, and these forces act on mutually opposite bodies. Newton’s Third Law of Motion tells us four characteristics: • Forces always occur in pairs. • Action and reaction forces are equal in magnitude. • Action and reaction forces act in opposite directions. • Action and reaction forces act on different bodies.

3. 3 Forces and Motion Newton’s Third Law (Optional) An example of action and reaction force is shown in the diagram above.

3. 3 Forces and Motion Key Ideas • The change in motion of an object is caused by unbalanced forces acting on it. • Forces acting on an object are balanced if the resultant force is zero. • Forces acting on an object are unbalanced if the resultant force is not zero. • Newton’s First Law states that every object will continue in its state of rest or uniform motion in a straight line unless a resultant force acts on it to change its state.

3. 3 Forces and Motion Key Ideas (continued) • Newton’s Second Law of Motion states that when a resultant force acts on an object of constant mass, the object will accelerate. The product of the mass and acceleration of the object is equal to the resultant force. In equation form, this is represened as F = ma • A resultant force is 1 N if the acceleration it produces on a mass of 1 kg is 1 m s-2. • Newton’s Third Law of Motion states that for every action, there is an equal and opposite reaction, and these forces act on mutually opposite bodies.

3. 3 Forces and Motion Test Yourself 3. 3 1. What can you deduce about the resultant force acting on an object that is (a) moving with constant speed in a straight line? (b) accelerating? Answer: (a) When an object is moving at constant speed in a straight line, then the resultant force F = 0. (b) If the object is accelerating, then there must be a resultant force. This resultant force F is given by F = ma.

3. 3 Forces and Motion Test Yourself 3. 3 2. An unloaded van has an acceleration of 5 m s-2. A fully loaded van weighs twice as much as the unloaded van. What is the acceleration of the fully loaded van if the forward thrust remains the same? Solution: Let a = acceleration of unloaded van a’ = acceleration of the fully loaded van m = mass of unloaded van Then, F = ma - - (1) F = 2 ma’ - - (2) Take equation (2) (1) 2 ma' 1 = ma a' = 1 a = 1 5 = 2. 5 m s-2 2 2

3. 3 Forces and Motion Test Yourself 3. 3 3. The Republic of Singapore Air Force uses the AIM-9 Sidewinder air-to-air missile, which has a mass of 86. 5 kg. If the missile can accelerate from 300 m s-1 to 700 m s-1 in 6 s, what is the average force exerted on the missile? Answer: v - u = 700 - 300 Acceleration of missile, a = t 6 = 66. 7 m s-2 By Newton’s Second Law, F = ma = 86. 5 66. 7 = 5770 N

3. 4 Friction and Its Effects Learning Outcomes In this section, you’ll be able to: • explain the effects of friction on the motion of a body • identify the forces acting on a body and draw free body diagrams • apply the relationship F = ma to solve related problems

3. 4 Friction and Its Effects How does friction affect motion? Friction always opposes motion between two surfaces in contact. The diagram below shows a microscopic view of two surfaces in contact.

3. 4 Friction and Its Effects of friction Friction has both positive and negative effects in our lives. Negative effects of friction • Friction reduces efficiency of cars by up to 20%. • Causes wear and tear of moving parts in engines, motors and machines. Positive effects of friction • Needed for walking or holding a pair of chopsticks • Used in braking pads to slow down cars

3. 4 Friction and Its Effects Friction as a negative force Friction causes wear and tear of moving parts in machinery. Ways to reduce friction include: • Wheels • Ball Bearings • Lubricants and polishing surfaces • Air cushion e. g. hovercraft and magnetic levitation in trains

3. 4 Friction and Its Effects Friction as a useful force Friction can also be useful for our daily lives. Examples include: • Car tyres • Parachutes • Rock climbing

3. 4 Friction and Its Effects Identifying forces and free body diagrams • Block diagrams with arrows used to represent forces acting on a body are called free body diagrams. • These diagrams help you to solve problems on forces in Physics.

3. 4 Friction and Its Effects An example of a free body diagram is shown below.

3. 4 Friction and Its Effects Key Ideas • Friction opposes motion between two surfaces in contact. • A non-zero resultant frictional force will cause a moving object to slow down to a complete stop. • There are both positive and negative effects of friction in our daily lives. • Free body diagrams are drawn to help us identify forces acting on a body or system of bodies, in order to solve problems.

3. 4 Friction and Its Effects Test Yourself 3. 4 1. Can you lean against a wall if frictional forces are absent? Answer: No. When you lean against the wall, the frictional force between your body and the wall, as well as the frictional force between your feet and the floor, keep you from slipping. 2. How can you reduce the effect of friction on the motion of a body? Answer: Using wheels, ball bearings and lubrication.

3. 4 Friction and Its Effects Test Yourself 3. 4 3. A force F of 50 N is needed to keep a trolley of mass 60 kg moving at a uniform velocity of 2 m s-1. What is the frictional force f on the trolley? a=0 F = 50 N Answer: friction f = ? Since the trolley is moving at uniform velocity, this means that acceleration a = 0. The resultant force is thus zero. Hence the pushing force F is equal to the friction force f. f = F = 50 N

3. 4 Friction and Its Effects Test Yourself 3. 4 4. A feather and a stone are released simultaneously from the same height. Explain why the feather will fall more slowly to the ground than the stone even though the acceleration due to free fall is the same for both the feather and the stone. fair stone W Answer: The air resistance fair experienced by the stone is relatively much smaller compared to its weight W. Hence the stone has an acceleration close to g, the acceleration due to gravity. fair W Answer: The feather experienced an air resistance fair that is quite comparable to its own weight W. Hence the feather’s acceleration is very low.

3. 5 Pressure Learning Outcomes In this section, you’ll be able to: • • Define the term pressure in terms of force and area force pressure = Recall and apply the relationship area to new situations or to solve related problems

3. 5 Pressure What is pressure? Pressure is defined as the force acting per unit area. force Pressure = area In symbols, p = where F A p = pressure F = force (in N) and A = area (in m 2)

3. 5 Pressure The SI unit of pressure is newton per square metre (N m-2) or pascal (Pa). You may have carried plastic bags filled with groceries before. If so, your fingers must have hurt! Padding the handles of heavy plastic bags helps to reduce the pressure acting on your fingers.

3. 5 Pressure Figure 7. 3(a) Figure 7. 3(b)

3. 5 Pressure