F O R C E S P A G E 1 L E A R N I N G O U T C O M E S Forces What is a force? Y E A R 9, C H A P T E R 2 G J Z A H R A B. E D ( H O N S ) How are forces measured? What do forces do? Why do we need to think of forces? What is meant by equilibrium? How do forces affect motion? What are scalars and vectors? What is a centre of gravity? How does the length of a spring vary with force? What is the difference between a stiff and a soft material? Why is rubber not used in car suspensions of other springs? What is a moment? How can a tight nut be loosened without applying too much force? Name and Surname: Class:
P A G E 2 2.1 What are Forces A force is something that causes a change in an object s motion (either speed or direction). This means that forces causes change, and without forces, things would not change. Forces can be simply thought of pushes and pulls and are measured in Newtons, N. One Newton is the force needed to change the speed of an object of 1 kg by 1m/s. An earthquake is a forceful event and causes lots of change Forces are represented scientifically as arrows, where the size of the arrow in a diagram is usually an indication of the size of the force. Forces are represented as arrows because they are vectors, meaning that they have both size and direction. Other measurements do not have a direction (area, volume, length, mass, speed) and are called scalar quantities. Measurements that have size and direction are called vectors. Measurements that have size only are called scalars. Scalars Vectors The centre of gravity of some regularly shaped objects 2.2 Weight and Centre of Gravity Weight is due to an object s mass and the pull of gravity of the planet. As seen earlier, weight can be found using the equation: W = mg Objects can be balanced on a point called the centre of gravity. When balanced, all the weight of the object seems to be concentrated at this point. The centre of gravity (cog) is the point from which all the weight of an object seems to act.
F O R C E S P A G E 3 For an irregular object this might be more difficult to calculate. If an object is hung from one side, it will equilibrate to a position where its centre of gravity is directly below the point from which it was hung. Thus, if an object is hung from more than one spot, different lines can be drawn to find where they intersect. This point of intersection is the centre of gravity of the object. The steps are as follows: Three or more holes are made in the irregularly shaped object The object is hung from a clamp together with a plumb-line and left to equilibrate Two marks along the plumb-line are marked A straight line passing through these marks is drawn using a ruler The steps are repeated for at least two more positions The point at which the three lines intersect is the centre of gravity of the object. Practice Exercise 2A What is meant by the centre of gravity of an object? Mark the centre of gravity of the following regularly shaped objects.
P A G E 4 2.3 Equilibrium When an object is not moving we say that it is at rest. At this stage, the forces on the object are said to be balanced or at equilibrium. There is no resultant force. If a large enough force acts on the body it will cause disequilibrium and the object will start moving with a particular speed and direction (velocity). Once the body is moving with constant velocity in the same direction, it is again in equilibrium. This means that no resultant force is acting on the body, as can be seen by the fact that there is no change in the body s velocity. Forces do not cause motion but changes in motion. In this case the backwards forces are provided by friction (resistance to motion due to physical contact with the ground or other objects) and air resistance or drag (resistance to motion due to gas or liquid particles through which the object is moving). This can be summarized in Newton s First Law of Motion: An object will remain at rest or moving at constant velocity in a straight line unless acted by an external, unbalanced force. If the object starts to slow down, change direction, or accelerate, it means that a resultant force is acting on the body causing disequilibrium. Newton s First Law of Motion states that the velocity of an object remains the same unless acted by an external, unbalanced force It follows that if an object is standing still on the ground, the force of weight is pushing the object down. However the object does not start to move. This means that the ground is exerting a force on the object, called the Reaction Force. Upthrust, or lift, is the force that pushes objects upwards in fluids (gases of liquids). Liquids exhibit more upthrust than gases, and this is why objects seem to have less weight in water. Weight and upthrust for an object at equilibrium The forces acting on a plane. If the opposite forces are equal, the plane could be either stationary or moving at constant velocity The reaction force on a runner s foot
F O R C E S P A G E 5 Forces and Equilibrium P R A C T I C E E X E R C I S E 2 B Answer the following questions 1. Define a scalar and a vector quantity. (3marks) 2. Classify the following quantities as scalars and vectors: (7marks) Length Time Weight Acceleration Displacement Velocity Volume 3. A parachutist of mass 75Kg jumps from an airplane. At the beginning he starts to accelerate downwards. Calculate and name the force acting on the parachutist downwards. (2marks) After some time, the parachutist stops accelerating and reaches constant speed. Draw and name the forces acting on the parachutist at this point in time. (2marks) What is the magnitude of the force acting upwards? (1mark) 4. Determine the tension in each cable in Case A and Case B shown in the diagram (3marks). 5. The force of gravity varies in different localities on Earth since the Earth is not a perfect sphere. It is lowest in Mexico where it is 9.779m/s 2 and highest in Oslo and Helsinki where it is 9.819m/s 2. Calculate the weight of a person of mass 75Kg at the two localities. (4marks) 6. The force of gravity on the moon is 1.6m/s 2. What mass would require a force of 700N to be lifted? (3marks)
P A G E 6 Name and Surname: Balanced and Unbalanced Forces A. The diagram shows an aeroplane with 4 forces acting on it P R A C T I C E E X E R C I S E 2 C 1. The aircraft is moving at a steady speed in a straight line. What is the magnitude of the frictional force (drag) 2. According to the diagram, which two forces are unbalanced? 3. What is the magnitude (size) and direction of the resultant force? B. The diagram shows a hot air balloon with 2 forces acting on it 1. Label the forces on the balloon 2. What is the size and direction of the resultant force acting on the balloon? 3. What is the effect of this unbalanced force? 4. The balloon continues to fall until the people inside start to throw out sand bags. With each bag of mass 12kg, how many bags do they need to throw out before they stop sinking in the air? M A R K S Question A 1 + 1 + 2 Question B 2 + 2 + 1 + 3 Question C 4 + 1 + 1 + 2 Total /4 /8 /8 /20 C. The diagram shows a submarine with 4 forces acting on it 1. Label the forces on the submarine. 2. What happens if the thrust is greater than the drag? 3. If the buoyancy force is less than the weight, what happens? 4. If the submarine wants to continue to move with a constant velocity at a given depth, what must happen to all the forces?
F O R C E S 2.4 Hooke s Law P A G E 7 Cars use helical springs for shock absorption Hooke s law states that the extension of a spring is directly proportional to the force causing it given that the elastic limit is not exceeded When a mass is attached to an object, the force downwards pulling the object might cause it to extend. This is very visible in springs; however it is also measurable in wires, rods and other objects. Robert Hooke studied elasticity and in 1678 published his findings that the extension of a spring is directly proportional to the force causing it given that the elastic limit is not exceeded. This means that, if a force of 10N causes a spring to increase in length by 0.01m, a force of 20N will cause the same spring to increase in length by 0.02m. Thus, if an object obeys Hooke s Law, a graph of force against extension should result in a straight line graph passing through the origin. Hooke s Law can be confirmed by an experiment where the extension of a spring for different forces is measured. These two variables are then plotted. The steps are as follows: A spring is attached with a clamp A pan is attached to the spring so that weights can be held here A pointer is also attached to make readings easier (precaution) The original length of the spring together wit the pan and pointer is measured with a ruler (precautions for the ruler must be applied) A weight is attached to the spring and the extension is measured and recorded. It is very important that the spring is left to reach equilibrium before measuring the extension (precaution) More weights are added and each time the extension is measured and recorded After adding a number of weights, these are removed one by one and the extension is again measured and recorded. This is done in order to take multiple readings for the same force (precaution) without restarting the experiment Care must also be taken not to add too much weights since the spring might be deformed (will not return to its original size) A graph of force (y-axis) against extension (x-axis) is plotted The apparatus for the experiment to confirm Hooke s Law
P A G E 8 Not all materials extend the same length for a given force. A material that does not extend a lot is called a stiff material. In this case, the gradient of the force-extension graph will be large. A material that extends a lot for a given force is said to be a soft material. In this case, the gradient of the forceextension graph is small. Sometimes, objects do not return to their original shape after being stretched or compressed by a force. This is because their elastic limit has been exceeded. The elastic limit of an object is the maximum stress that can be applied to the object without permanently changing its shape. Once this limit is exceeded, the spring will be denatured and will not return to its original shape. Even if an object can continue to be extended after its elastic limit has been exceeded, Hooke s law is no longer obeyed after this point and the graph curves. Note that the elastic limit is not the breaking point, which is the force needed to break the spring. Some materials, such as rubber, do not obey Hooke s law. This is easily observable from the graph obtained for the extension of rubber against force applied. The point marked as failure indicates where the material breaks. Practice Exercise 2D The table below was obtained from an experiment as described in the previous page. Use these results to plot a graph of Force (N) against Extension (m). Does the spring obeys Hooke s Law? Calculate the gradient of the graph. Mass/ kg Length/ m 0 0.13 100 0.30 200 0.46 300 0.62 400 0.80 The stiffer the material, the larger the gradient of the Force-Extension graph is, showing a smaller extension for the same force After exceeding the elastic limit, the object no longer obeys Hooke s Law and the graph is no longer linear. Rubber does not obey Hooke s Law and the extension and the force causing it are not directly proportional
F O R C E S P A G E 9 Hooke s Law - Simulation Instructions G J Z A H R A B. E D ( H O N S ) S T A L B E R T T H E G R E A T C O L L E G E P R A C T I C E E X E R C I S E 2 E 1. Open the site http://phet.colorado.edu/sims/mass-spring-lab/mass-spring-lab_en.html 2. Move the ruler (by dragging) beside spring 1. Align the 0cm mark with the dotted line. 3. Hang the 50g mass with spring 1. Let the spring to equilibrate and measure the extension. 4. Repeat step 3 for the 100 and 250g masses. 5. Copy and complete the table below. Mass (g) Mass (kg) Weight (N) Extension (cm) Extension (m) 50 0.05 0.5 100 250 6. On a graph paper, plot a graph of Force (N) on the y-axis against Extension (m) on the x- axis. Remember to use a sharp HB pencil, to label each axis and to name the graph. 7. Find the gradient of the graph and determine its units 8. Set the softness of spring 3 to hard 9. Repeat the experiment (steps 2-7) with spring 3 set to hard. Fill in another table of results as in step 4 and plot a graph on the same graph paper used in step 6. 10. Calculate the gradient of the hard spring. Compare this value to the one of the soft spring. What do you note? 11. Still using the hard spring, attach the masses of unknown mass and measure the extension of the spring. Fill this information in the table below. Unknowns Extension (cm) Extension (m) Green Brown Red 12. Using the graph plotted in step 9, find the weight of these unknown masses. 13. Would you expect spring 3 to stretch more on the moon? Why? Try it out!
P A G E 10 2.5 Moments When a force is not applied on the centre of gravity of an object it will give rise to a turning effect, which might result in the object to rotate or twist. The turning effect of a force is called a moment. For a moment to be present, a force must be applied at a distance from a pivot A moment is the turning effect of a force. At equilibrium, the total clockwise moment equals the total anticlockwise moment. Sometimes one is unable to turn a tight nut with a wrench. What people usually do is attach a pipe to the wrench so that the handle is lengthened. This is because the moment and distance from the pivot are directly proportional according to the equation: M = moment, in Nm M = Fd F = Force applied perpendicular to pivot, in N d = distance of force from the pivot, in m 2.6 Moments and Equilibrium If moments are applied to the same side of the pivot, they will add up to each other. Moments on the other side, however, have an opposite turning effect so they are subtracted. Thus, the direction of a moment must always be specified (moments are vector quantities). Moments are said to be either clockwise or anticlockwise. For a system to be at equilibrium (no rotational motion) the total clockwise moment must be equal to the total anticlockwise moment. In summary, if we look at the (very complicated) example below: Total clockwise moment (CM) = (F 1 *d 1 ) + (F 2 *d 2 ) + (F 3 *d 3 ) Total anticlockwise moment (ACM) = (F 4 *d 4 ) + (F 5 *d 5 ) Maximum and zero moment on a bicycle pedal
F O R C E S P A G E 11 Moments P R A C T I C E E X E R C I S E 2 F Solve A, B, C and D for the following systems at equilibrium
P A G E 12 Moments Answer the following questions 1. A metre rule is balanced from its centre. A weight of 2N is placed on the right hand side 0.30m from the pivot. Another weight, W, is placed on the opposite side 0.40m from the pivot in order to balance the ruler. Draw a diagram to show this apparatus. Calculate the moment produced by the 2N weight. State the principle of moments. Calculate the weight, W. 2. The diagram below shows a worker using a lever of negligible weight to lift a heavy rock of mass 70kg. The object is 0.3m from the fulcrum while the worker applies force at 1.4m from the pivot. Calculate the minimum amount of force needed to life the stone. 3. A uniform metre rule is balanced at the 20cm mark by placing a mass of 200g at the 0cm mark. Calculate the mass of the ruler. 4. The diagram shows a simple machine to lift water from a pond P R A C T I C E E X E R C I S E 2 G Calculate the moment due to the bucket of water What is the total anti-clockwise moment if the system is balanced? For the system to be balanced, the man exerts a force of 80N. If the beam is uniform, calculate the weight of the beam (hint: you need to find the distance between the COG and the pivot). What is the upward reaction force at the pivot if the system is balanced?