New Senior Secondary Physics Compulsory: Mechanics Chapter ... · PDF fileNew Senior Secondary Physics Compulsory: Mechanics Chapter 3 Force and Motion Page 6 4 Resolution of forces

New Senior Secondary Physics Compulsory: Mechanics Chapter 3 Force and Motion

Page 1

CHAPTER 3 FORCE AND MOTION

1 Newton’s First Law of Motion

Why moving objects stops in real life? A wooden block is sliding on a horizontal table. Why the block stops eventually?

Free object What if the table is frictionless?

Newton’s First Law of Motion

Inertia

Measure of Inertia


Page 2

2 Newton’s Second Law of Motion Why objects move? A wooden block is at rest on a smooth horizontal table. How to make it moves?

Effect of force

The effect of mass

Newton’s Second Law of Motion


Page 3

[Simple calculation] A wooden block of mass 2 kg is placed on a table. A force of 50 N is applied on the block as shown below.

(a) If the table is smooth, what is the acceleration of the block?

(b) If the friction between the block and the table is 8 N, what is the acceleration of the block?

3 Free body diagram and common forces

[Concept] Draw the free body diagram of the wooden block in the previous question.

50 N


Page 4

Weight

Normal reaction force

Weight vs Mass

Friction

Tension


Page 5

[Concept] A ball rests on the ground. Draw its free body diagram and label all forces.

[Concept] A ball is thrown vertically upwards. Draw the free body diagram and label all forces when the ball is at its maximum height.

[Concept] A wooden block rests on a rough inclined plane. Draw its free body diagram and label all forces.


Page 6

4 Resolution of forces and equilibrium [HKCEE] Three forces of magnitude F1, F2 and 10 N act on object as show above. If the object is in equilibrium, find 1F and 2F .

Equilibrium What can we say when an object is under force equilibrium?

[HKCEE] Two forces F1 and F2 act on a particle P shown above. If a third force F3 acts on P to keep it in equilibrium, find the magnitude of F3.


Page 7

[HKCEE] A light rope is fixed at two poles with ends A and B at the same level. A T-shirt of weight 2 N is hung at the midpoint C of the rope. The rope depresses such that ∠ ACB = 150º. Find the tension in rope.

[Unbalanced force][HKCEE] Which of the following objects are under the action of an unbalanced force at the instant shown in the diagrams?


Page 8

5 Newton’s Third Law of Motion

Newton’s Third Law of Motion

Action and reaction pair

Example of Action and reaction pair A fan cart is accelerating forward by propelling wind on a smooth surface. Draw its free body diagram and identify all the action and reaction pairs.


Page 9

Example of Action and reaction pair A boy is sitting on a chair, draw his free body diagram and identify all the action and reaction pairs.

[Action and reaction pair][HKCEE] A block is placed on a table resting on the ground as shown in Figure (a) above. Figure (b) shows the forces acting on the block and the table respectively.

Let F1 = weight of the block F2 = force exerted by the block on the table F3 = force exerted by the table on the block Which of the following statements are correct? (1) F1 and F2 represent the same force (2) F1 and F3 balance each other (3) F2 and F3 form an action-reaction pair


Page 10

[Action and reaction pair][HKCEE]

Figure 3 shows a water rocket. The rocket is filled with water and compressed air. Explain why the rocket rises when the trigger is pulled and name the law or principle involved. (4 marks)


Page 11

6 Common dynamical systems

6.1 Simple block [Concept] A 8kg wooden block on a smooth horizontal table is pulled by a force of 100N. (a) If the force is horizontal, what is the acceleration of the block? (b) If the force is inclined at 30o to the horizontal, how will the block move? Will the block be pulled

upwards?

(c) If the magnitude of the force is kept at 100N , at which angle will the block start to move upward?


Page 12

6.2 Connecting blocks [Simply connecting block]

Two blocks are connected by a light string S. A horizontal force F is applied to the 2 kg block. If

30F N= , (a) Draw the free body diagram of the 4kg block. (b) Draw the free body diagram of the 2kg block. (c) What is the acceleration of the blocks? (d) Find the tension in the string.


Page 13

[Contacting blocks]

Two blocks, A and B, or masses 1kg and 3kg respectively, are placed on a horizontal surface as shown. A horizontal constant force of 12 N is applied to block A so that the two blocks move to the right together. If all contacting surfaces have friction 1N. Find the acceleration of the blocks and the magnitude of the contacting force between A and B?


Page 14

[Pulley system]

Two blocks are connected by a light smooth pulley with 4kg mass Y hanging freely and 8 kg mass X initially rests on a table. Friction between X and the table is 5N. (a) Draw the free body diagram of block Y. (b) Draw the free body diagram of block X. (c) Find the acceleration of the blocks and the tension in the string.


Page 15

6.3 Inclined plane and friction compensated runway

[Inclined plane] A 4 kg block rests on a plane inclined at 25o

θ= to the horizontal.

(a) Draw the free body diagram of the block. (b) Find the friction between the block and the plane.


Page 16

[Inclined plane]

A block of mass 0.5 kg slides down a rough inclined plane with an acceleration of 3 ms-2. If the plane is inclined at 30° to the horizontal, find the friction between the block and the plane.

Friction compensated runway A block of mass 2 kg rests on a rough inclined plane with friction 10N. The inclination of the plane is carefully adjusted so that the block is about to move. Find the value of θ .


Page 17

[Friction compensated runway][HKCEE] The figure shows a trolley running down a friction compensated runway. The trolley is connected to a hanging weight by means of a light inelastic string. A card of width 0.03 m is attached to the trolley. Light sources S and light detectors D are fixed at two positions A and B along the runway. Each light detector is connected to a timer, which can measure the time taken by the card to pass the light detector. (a) The timers record that it takes 0.050 s and 0.025 s for the 0.03 m card to pass the light detectors at A and B respectively. (i) Calculate the average speed of the trolley as it passes (1) Position A, and (2) Position B. (3 marks) (ii) If the mass of the trolley is 1.5 kg and the distance between A and B is 0.4 m, Calculate: (1) The acceleration of the trolley, (2) The tension in the string. (5 marks)


Page 18

(b) Describe how you can use a stroboscopic camera to check whether the runway is friction compensated. (4 marks) (c) If the string suddenly breaks, describe the subsequent motion of the trolley along the runway. (1 mark)


Page 19

6.4 Air resistance and terminal speed

Air resistance: Light vs heavy objects [Theoretical calculation] A light ball of mass m and a heavy ball of mass M of the same shape are released at the same height h . (a) If air resistance is negligible, show that they both hit the ground at the same time.

(b) By considering the effect of air resistance f , show that the lighter mass will reach the ground at a much longer time and the heavy mass is not quite affected.


Page 20

Air resistance: Terminal Velocity [Theoretical calculation] A sky diver jump off the helicopter at 0t= . She falls freely under gravity and resisted by air. If the air resistance f is assumed to be directly proportional to her speed, i.e. f kv= for some constant k , (a) Show that the sky diver will have her speed increased quickly at the beginning of her dive.

(b) Show that her downward acceleration decreases as she gains her speed.

(c) Show that she eventually falls with a constant speed.

(d) Finally she opens her parachute and land safely. Draw her v t− graph from 0t= until she land.


Page 21

6.5 Lift, apparent weight and weightlessness

Lift system A man is standing on a weighing scale inside a lift. Draw the free body of the man and the weighing scale when the lift is at rest.

Weight vs Apparent weight Does his weight always equal to his apparent weight? Which quantity is the feeling of ‘weight’ that the person usually feels?

Reading of weighing scale In a common weighing scale, which physical quantity is it measuring and how does it relate to your body mass?


Page 22

Apparent change of weight in a lift How does the apparent weight of the man change when the lift is (a) accelerates upwards / decelerates downwards (b) accelerates downwards / decelerates upwards (c) What if the lift accelerates downwards at 29.81 ms− ?


Page 23

7 Moment of a force and mechanical equilibrium

Moment of a force / Torque

Conditions for mechanical equilibrium

[Concept] Calculate and determine whether the following weightless rod is at mechanical equilibrium.


Page 24




Page 25

[Beam]

A workman of weight 800N stands on a wooden beam of length 4 m and the beam weighs 100N. The beam, with its centre of gravity in its middle, is supported by its two ends. The workman is 1m from the end of the beam. Find the reaction forces X and Y. [Further question: if the workman walks towards B, what will be the changes in the values of X and Y?]


Page 26

[Beam][HKCEE]

A uniform plank of weight 450 N rests on two trestles X and Y and a worker of weight 675 N stands at one end of the plank as shown above. The worker holds a light basket which contains several packets of goods each of weight 6 N. What is the maximum number of packets he can hold without tilting the plank? (Assume the weight of the plank acts through its centre.)


Page 27

FINAL REMARKS

This chapter is the MOST IMPORTANT CHAPTER in mechanics, and even in the whole syllabus of physics! Newton’s laws of motion give answers to important questions like ‘why objects move?’ and ‘how different objects interact?’ These laws can be used to analyze basically ALL mechanical systems and this lays the foundation of classical physics. A wide range of mechanical phenomena can be explained under Newtonian mechanics.

Basically everything in this chapter are important, both on its own and later chapters. Students should try their best to understand the chapter content and try to apply them to daily life. If you do not understand this chapter, you must resolve your puzzle as early as possible. It is fair to say that you are quite hopeless, if not impossible, to get a pass in physics if you find yourself do not understand F ma= . On the other hand, if you find this chapter

comfortable, you will find most of the subsequent chapters comprehensible and easy to grasp.

Documents

New Senior Secondary Physics Compulsory: Mechanics Chapter ... · PDF fileNew Senior Secondary Physics Compulsory: Mechanics Chapter 3 Force and Motion Page 6 4 Resolution of forces