CHAPTER 3 Forces 2013 Marshall Cavendish International Singapore

CHAPTER 3 Forces © 2013 Marshall Cavendish International (Singapore) Private Limited

Founder of Force • • • Sir Isaac Newton 1643 -1727 Father of Classical Physics Cambridge University Mechanics & Motion He was sitting below an apple tree when something miraculous happened.

Chapter 3 Forces 3. 1 Forces 3. 2 Free-Body Diagrams 3. 3 Vector Diagrams 3. 4 Forces and Motion 3. 5 Friction and Its Effects

3. 1 Forces What are Forces? • A force is a push or a pull that one object exerts on another. Its SI unit is the newton (N). • A force can produce, slow down, speed up, or stop motion. It can also change the direction of motion. • Forces can be classified as follows: Contact forces Non-contact forces Normal reaction Gravitational force Friction Electric force Tension Magnetic force

3. 1 Forces Worked Example Consider a car moving along a rough road. What forces can you think of that are acting on the car? Solution • Force of engine • Weight • Friction • Normal reaction • Air resistance air resistance friction normal reaction force of engine weight car in motion

Chapter 3 Forces 3. 1 Forces 3. 2 Free-Body Diagrams 3. 3 Vector Diagrams 3. 4 Forces and Motion 3. 5 Friction and Its Effects

3. 2 Free-Body Diagrams Learning Outcome At the end of this section, you should be able to: • identify the forces acting on a body and sketch a freebody diagram to represent them.

3. 2 Free-Body Diagrams • Free-body diagrams are simple diagrams with arrows that represent forces acting on individual objects. • To draw a free-body diagram, we must first identify all the forces acting on each object. • Examples of free-body diagrams: tension box suspended by strings force of engine rocket in flight weight air resistance

3. 2 Free-Body Diagrams Worked Example A car is moving to the right with uniform speed on a rough road before its engine is switched off. Draw a free body diagram to illustrate the forces acting on the car after its engine is switched off. Solution normal reaction friction weight car slowing down on a rough road

3. 3 Vector Diagrams Learning Outcomes At the end of this section, you should be able to: • add two vectors using a graphical method; • solve problems that involve three forces on a static body using a graphical method.

3. 3 Vector Diagrams Recall • Scalar quantities are physical quantities that have magnitude only. • Vector quantities are physical quantities that have both magnitude and direction. • When we add 5 m 3 of water to another 5 m 3 of water, we get 10 m 3 of water. • What do we get when we add a 5 N force to another 5 N force? Is force a scalar or a vector? How do you add forces?

3. 3 Vector Diagrams A Vector Diagram Let’s represent a force of 20 N that acts in the direction of 45˚ North of East. N 4 cm Scale 1 cm : 5 N 45˚ We denote a vector with an arrow to indicate its direction.

3. 3 Vector Diagrams Addition of Vectors • When more than one vector acts on an object, we must find a single vector, the resultant vector, that produces the same effect as the individual vectors combined. • For parallel vectors, how do we find the resultant vector? • A resultant vector is represented by a double-headed arrow.

3. 3 Vector Diagrams Addition of Vectors When vectors are not parallel, how do we find the resultant vector? Parallelogram method 5 N Tip-to-tail method 7 N 40˚ 18˚ 20˚ 3 N 3 N 5 N Scale 1 cm : 1 N 18˚ 20˚ 7 N URL

Chapter 3 Forces 3. 1 Forces 3. 2 Free-Body Diagrams 3. 3 Vector Diagrams 3. 4 Forces and Motion 3. 5 Friction and Its Effects

3. 4 Forces and Motion Learning Outcomes At the end of this section, you should be able to: • apply Newton’s laws of motion to - describe how a force may change the motion of a body; - describe the effects of balanced and unbalanced forces on a body; - identify action–reaction forces acting on two interacting bodies. • apply the formula resultant force = mass × acceleration to solve problems.

3. 4 Forces and Motion Recall • When the speed and/or direction of an object changes over a period of time, there is acceleration. • Acceleration = change in velocity time taken How is the motion of an object affected when a force acts on it?

3. 4 Forces and Motion Effects of a Force Applying a force can cause an object to accelerate. A force applied on… a stationary object can cause it to… start moving a moving object increase its speed a moving object decrease its speed a moving object change its direction When the acceleration of an object is zero, does this mean there is no force acting on the object?

3. 4 Forces and Motion Effects of a Force • Zero acceleration means the object can be stationary, or moving with a constant velocity. • This does not mean there are no forces acting on the object. • Instead, it means the resultant or net force is zero. • The motion of objects is governed by Newton’s laws of motion. URL

3. 4 Forces and Motion Newton’s First Law of Motion 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. • If the resultant force acting on an object is zero, the forces acting on the object are balanced, and there is no acceleration.

3. 4 Forces and Motion Newton’s First Law 0 m s− 1 • Car is stationary • Are there horizontal forces acting on it? Answer: No Resultant force = 0 N 2 m s− 1 • Car is moving with constant velocity • Are there horizontal forces acting on it? Answer: Yes • What are the forces? • Driving force and frictional force • Since velocity is constant, Driving force = Frictional force Resultant force = 0 N

3. 4 Forces and Motion Newton’s First Law • A box that is stationary remains at rest, unless it experiences a resultant force. • Weight W of the box is balanced by normal reaction F from the table. • A box moving with a constant velocity on a smooth, horizontal surface continues to travel in a straight line at the same speed, unless it experiences a resultant force. F W

3. 4 Forces and Motion Question A boy is pushing a box at a constant speed on a straight path. Which statement describe the horizontal forces acting on the box correctly? (A)The pushing force is equal to the frictional force. (B)The pushing force is greater than the frictional force. (C)There are no horizontal forces as the speed is constant. (D)Cannot be described as the magnitude of the forces are not given.

3. 4 Forces and Motion Question A hockey puck lies at rest on a perfectly smooth surface. You give the hockey puck a quick push. The force acts on the hockey puck momentarily. Describe the subsequent motion of the hockey puck. (A)Moves with increasing speed in a straight line (B)Moves with constant speed in a straight line (C)Decelerates uniformly to rest (D)Cannot be determined as magnitude of force is not given

3. 4 Forces and Motion Newton’s Second Law of Motion states that The product of the mass and acceleration of the object gives the resultant force. • If the resultant force acting on an object is not zero, the forces acting on the object are unbalanced, and there is acceleration.

3. 3 Forces and Motion Newton’s Second Law • In symbols, Force = mass x acceleration where F = resultant force (in N); m = mass of object (in kg); a = acceleration of object (in m s– 2).

3. 4 Forces and Motion Newton’s Second Law 2 m s− 2 • If you step on the accelerator, the car speeds up (or accelerates). • What is happening in terms of forces? • Driving force > Frictional force • Resultant force > 0 N • Therefore, the car accelerates in the direction of the resultant force.

3. 4 Forces and Motion Newton’s Second Law • Friction exists in the real world. • If a box is given a push that is greater than the friction it experiences, the forces that act on the box are unbalanced (in the horizontal direction). • The box experiences a non-zero resultant force, which is directed towards the right. acceleration F push friction W • This resultant force causes the box to accelerate to the right, in the direction of the resultant force.

3. 4 Forces and Motion Newton’s Second Law • If the push is removed, only friction acts on the box (in the horizontal direction). Friction becomes the non-zero resultant force acting on the moving box. • The resultant force is now directed towards the left. acceleration F friction W • This resultant force causes the box to accelerate to the left (or decelerate to the right), in the direction of the resultant force. The box comes to a stop after a while.

• Virtual Lab • http: //glencoe. mheducation. com/sites/00786 17707/student_view 0/chapter 2/virtual_lab. ht ml

3. 4 Forces and Motion Worked Example A car of mass 1000 kg travels on a smooth road at a constant velocity of 50 km h– 1. It experiences an engine force of 5000 N. What is the resultant force that acts on the car? Solution The resultant force is zero. The car travels at constant velocity, so it is not accelerating. The absence of acceleration means there is no resultant force acting on the car.

3. 4 Forces and Motion Worked Example A car of mass 1000 kg accelerates from rest to 20 m s– 1 in 5 s. Calculate the resultant force that acts on the car when the car is travelling on (a) a smooth road. Solution change in velocity Acceleration = time taken 20 m s– 1 – 2 a= = 4 m s 5 s Resultant force F = ma = 1000 kg × 4 m s – 2 = 4000 N

3. 4 Forces and Motion Worked Example A car of mass 1000 kg accelerates from rest to 20 m s– 1 in 5 s. Calculate the driving force that acts on the car when the car is travelling on (b) a rough road that exerts friction of 50 N on the car. Solution Resultant force = Driving force – frictional force Driving force = Resultant force + frictional force = 4000 N + 50 N = 4050 N

3. 4 Forces and Motion Worked Example A car of mass 700 kg can exert an engine force of 5000 N. When it travels along a road, it experiences friction of 100 N. (a) Draw a free-body diagram to show the forces acting on the car. Solution normal reaction force of engine = 5000 N friction = 100 N weight

3. 4 Forces and Motion (b) Using the free-body diagram, calculate the resultant force and the acceleration. Solution force of engine = 5000 N friction = 100 N Resultant force = force of engine – friction = 5000 N – 100 N = 4900 N Acceleration = resultant force mass = 4900 N 700 kg = 7 m s – 2

3. 4 Forces and Motion Newton’s Third Law of Motion states that for every action, there is an equal and opposite reaction. This tells us four characteristics of forces: • Forces always occur in pairs. Each pair is made of an action and a reaction. • Action and reaction are equal in magnitude. • Action and reaction act in opposite directions. • Action and reaction act on different bodies.

3. 4 Forces and Motion Newton’s Third Law A box rests on a table. Can you identify the pairs of action reaction forces? Weight W of the box and normal reaction F are an action–reaction pair. F • W has the same magnitude as F, so the box is at rest. • W acts vertically downwards, while F acts vertically upwards. • W acts on the table due to the box, while F acts on the box due to the table. W

3. 4 Forces and Motion Newton’s Third Law A box rests on a table. Gravitational force of Earth on box (FEB) and the gravitational force of box on Earth (FBE) are an action–reaction pair. • FEB has the same magnitude as FBE, so the box is at rest. • FBE acts vertically downwards, while FEB acts vertically upwards. • FBE acts on the box due to the Earth, while FEB acts on the Earth due to the box. FBE FEB

Chapter 3 Forces 3. 1 Forces 3. 2 Free-Body Diagrams 3. 3 Vector Diagrams 3. 4 Forces and Motion 3. 5 Friction and Its Effects

3. 5 Friction and Its Effects Learning Outcome At the end of this section, you should be able to: • explain how friction affects the motion of a body.

3. 5 Friction and Its Effects Friction • Friction is the contact force that opposes or tends to oppose motion between surfaces in contact. • Friction is the result of irregularities of surfaces. • There are positive and negative effects of friction: moving vehicles are able to slow down when needed, but moving parts in engines, motors, and machines suffer wear and tear. How does friction cause these effects?

3. 5 Friction and Its Effects Example friction • To move to the right, the wheel has to rotate in a clockwise direction (green arrow). • Friction opposes motion, therefore it acts to the right (shown by the red arrow). friction • To move to the right, the foot has to push backwards on the ground (green arrow). • Friction opposes motion, therefore it acts to the right (shown by the red arrow).

3. 5 Friction and Its Effects Reducing Negative Effects of Friction • Wheels The circular shape of wheels reduces the area of the contact surfaces. With less friction, a smaller force is needed to move a shopping trolley. • Ball bearings Spherical ball bearings work like wheels. They roll around, and prevent moving surfaces in machines from rubbing against each other directly.

3. 5 Friction and Its Effects Reducing Negative Effects of Friction • Lubricants and polished surfaces These smooth over or remove surface irregularities, so engine surfaces in contact experience less friction when they move against each other. • Air cushion A layer of air between surfaces reduces friction, so a hovercraft can travel faster.

3. 5 Friction and Its Effects Enhancing Positive Effects of Friction • Treads These channel water out from under tyres, which improves the tyres’ grip on the road surface, and prevents vehicles from skidding. • Parachute The large air resistance created by the canopy of an open parachute slows down a descending parachutist, so that he may land safely. • Chalk Rock climbers apply chalk powder to their palms to absorb sweat, and hence improve their grip.

Chapter 3 Forces (SI unit: N) affect Newton’s First Law of Motion of objects Newton’s Second Law of Motion applies to resultant force = 0 N Balanced forces At rest describes resultant force ≠ 0 N Action– reaction pairs Unbalanced forces for a body Moving at a constant velocity Acceleratin g Newton’s Third Law of Motion Decelerating