2.8 Understanding Gravity

2.8 Understanding GravityChapter 2 Forces and MotionWhen a boy accidentally drop books from his hand.The books drop to the ground.

The book is pulled towards the Earth by the force of gravity.

The force of gravity on the Earth is caused by a gravitational field around the Earth.

The direction of the gravitational field.

Acceleration due to gravityA coin and a feather.Both the coin and the feather are released simultaneously from the same height.What will happen?

The air resistance to the feather is greater than the air resistance to the coin.The feather falls with a smaller acceleration and takes longer time to reach the ground.

What happen if it happen in a vacuum?Vacuum in the absence of air resistance

In airIn Vacuum

Put a coin and a feather into the tube (see diagram). Close one end with a rubber stopper, the other end with a bung having a small tube with a clip for pumping the air out.Hold the tube vertically so that both the coin and feather fall to one end. Now invert the tube quickly and observe the fall of the coin and the feather in the tubeIn Vacuum in the absence of air resistanceIn a vacuum, both the coin and the vacuum would fall with the same acceleration regardless of their shapes or masses.

Elephant and Feather - Free Fall

A free-falling object is an object falling under the force of gravity only.A free-falling objects does not encounter other forces like air resistance or friction that would oppose its motion.

The motion of the elephant and the feather in the absence of air resistance is shown. Further, the acceleration of each object is represented by a vector arrow.Many people are surprised by the fact that in the absence of air resistance, the elephant and the feather strike the ground at the same time.On earth, all objects (whether an elephant or a feather) have the same force of gravity.

Stroboscopic photographA stroboscopic photography is a photography that shows the image of an object in motion.The images are taken at regular time intervals.

Figure shows a stroboscopic photography of two steel spheres (of different sizes) falling under gravity.The two spheres are dropped simultaneously from the same height.The time intervals between two successive images are the same.Two inferences can be made from the photograph.

Inferences 1Two spheres are falling with an acceleration.The distance between two successive images of each sphere increases, showing that the two spheres are falling with increasing velocity, i.e. accelerationThe two spheres are falling with same acceleration. Thus, a heavy object and a light object fall with the same gravitational acceleration.In other words, gravitational acceleration is independent of mass.

Air resistanceAir resistance depends on the shape or cross-sectional area of the falling object.Air resistance also increases with the velocity of the falling object. An object moving at a higher velocity encounters greater air resistance than a similar object moving at a lower velocity.For a compact falling object, its acceleration has almost the same value as the gravitational acceleration. However, a light object like a piece of paper or a feather does not undergo free fall.This is because of the large air resistance that acts against it when it falls.

Acceleration of GravityFigure shows that all objects are pulled towards the centre of the Earth by the force of gravity.The objects will falls with an acceleration of 9.8 ms-2 due to the pull of this gravitational force.Since this acceleration is due to the force of gravity, it is called the gravitational acceleration.The gravitational acceleration is denoted by the symbol, gActivity 2.5 To determine the value of gravitational acceleration, gApparatus / Materials:Ticker-timer with carbonised tape, power supply, retort stand, slotted weights with holder, G-clamp, cellophane tape and soft board.

Procedure1. A ticker-timer is clamped to a retort stand with a G-clamp and placed on a tabletop.2. One end of a carbonised ticker tape (approximately 1.5 m in length) is attached to a weight holder with a total mass of 200 g.3. The other end of the ticker tape is passed through the ticker-timer.4. A soft board is placed on the floor below the weight to stop its fall.5. The ticker-timer is switched on and the weight is released so that it falls squarely onto the soft board.6. Six strips are cut off from the middle section of the ticker tape with each strip containing 2 dot-spaces.7. A tape chart is construed. Form the chart, the acceleration of gravity is calculated.Weight and Gravitational AccelerationThe weight of an object is defined as the force of gravity which is exerted on it by Earth.From the formula, F = maSince weight , W, is the force of gravity acting on an object of mass, m, that makes it fall with an acceleration, g, therefore, using the corresponding terms,W = mgWeight = Mass x Acceleration due to gravityGravitational Acceleration & Gravitational Field StrengthGravitational Acceleration & Gravitational Field StrengthExampleMass & WeightMass, mThe mass = amount of matterThe mass is constant everywhereA scalar quantityA base quantityUnit: kilogram (kg)Weight, WThe weight = force of gravity The weight is varies with the magnitude of gravitational field strength, g of the location.A vector quantityA derived quantityUnit: newton (N)

Equations of motion with constant accelerationSome recommend changing the acceleration, a in the equations to g, but this is not necessary.Simply bear in mind that while solving problems involving free fall, the acceleration, a in the equations has a value of:a = 10ms-2(for downward motion) a = - 10ms-2(for upward motion)

Example1. Ali is a basketball player. His vertical leap is 0.75 m. What is his take-off speed?

2. A coconut takes 1.5 seconds to fall to the ground. What is(a) its speed when it strikes the ground?(b) the height of the coconut tree?3. After winning a game, a pitcher throws a baseball vertically up with a velocity of 30 ms-1(a) What is the time taken for the ball to reach the maximum height?(b) What is the speed of the baseball when it returns to his hand?(c) How long is the ball in the air before it comes back to his hands?Problems Involving F = ma and W =mgLift

Weighing machinereading on the scale shows the normal reaction force, RW = true weight = mgR = normal reaction force exerted on the girl by the platform of the scale

1. When a girl stands on the platform of a weighing scale, there are two forces acting on her:(a)the girls weight, W (= mg) acting downwards,(b)the upward normal reaction force, R exerted on her feet by the platform of the scale2.The reading of the scale gives the value of the normal reaction force, R.Different situation in the lift,

Lift at rest or moves up or down at a constant velocityWhat is the reading shows at scale?Lift moves up at an acceleration of a ms-2

What is the reading shows at scale?

Lift moves down at an acceleration of a ms-2

What is the reading shows at scale?

Help! I am floating!What is the apparent weight of a girl on a weighing scale in a lift if the cable of the lift suddenly breaks?A student of mass 50 kg stands on weighing scale in a lift. If the reading on the scale becomes 550 N, is the lift accelerating upwards or downwards? Find the magnitude of the acceleration of the lift.Problems Involving F = ma and W =mgPulley system

Pulley systemA frictionless pulley serves to changes the direction of a force.The tension, T that results from the pulling at the ends of the string or rope has the same magnitude along its entire length.2 type of pulley system(A)A force pulling a mass over a pulley(B)A pulley with two masses

(A)A force pulling a mass over a pulleyIn this situation, the tension T, is equal to the pulling force F, even if the rope is slanting

A boy is pulling a bucket filled with sand. The mass of the bucket with the sand is 3 kg. Find the tension in the rope if the bucket is(a)stationary(b)moving up with a constant acceleration of 2 ms-2

(B)A pulley with two massesThe heavier mass will accelerate downwards while the lighter one will accelerate upwards with the same magnitude.The tension is not equal to the weight of either mass.

Two masses of 5kg and 3 kg are connected to a rope which passes over a frictionless pulley.Find the tension in the rope and the acceleration of the 3kg when 5kg mass is released.

A 2 kg weight is connected by a rope to a 3 kg wooden block. The rope passes over a smooth pulley .The weight is then released. Find the tension in the rope if a friction of 5N acts against the wooden block.