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A stationary object remains stationary if the sum of the forces acting upon it - resultant force - is zero. A moving object with a zero resultant force keeps moving at the t he same speed and in the same direction. Acceleration depends on the force applied to an object and the object's mass. Gravity is a force that attracts objects with mass towards each other. The weight of an object is the force acting on it due to gravity.
esultant force You should be able to use the idea of the resultant force on an object to determine its movement. An object may have several different forces acting on it, which can have different strengths and directions. They can be added together to give theresultant theresultant force. force. This is a single force that has the same effect on the object as all the individual forces acting together. together. !hen the resultant force is zero
When all the forces are balanced, the resultant force is zero. In this case: •
A stationary object remains stationary A moving object ee!s on moving at the same s!eed in the same direction
"or e#am!le, in the diagram of the weightlifter, the resultant force on the bar is zero, so the bar does not move. Its weight acting downwards is balanced by the u!ward force !rovided by the weightlifter. The longer the arrow, the bigger the force. In this diagram, the arrows are the same length, so we now they are the same size. !hen the resultant force is not zero
When all the forces are not balanced, the resultant force is not zero. In this case: •
A stationary object begins to move in the direction of the resultant force A moving object s!eeds u!, slows down or changes direction de!ending on the direction of the resultant force In this diagram of the weightlifter, the resultant force on the bar is not zero. The u!wards force is bigger than the downwards force. The resultant force acts in the u!wards direction, so the bar moves u!wards.
In this ne#t diagram of the weightlifter, the resultant force on the bar is also not zero. This time, the u!wards force is smaller than the downwards force. The resultant force acts in the downwards direction, so the bar moves downwards. This can be shown with numbers in a calculation. If the u!wards force was $ % and the downward force & % then the resultant force would be
' % (the difference between the two forces). It would act in a downwards direction.
esultant forces and motion You should now that objects accelerate when the resultant force is not zero, and understand the factors that affect the size of the acceleration. "ize of the force An object will accelerate in the direction of the resultant force. The bigger the force, the greater the acceleration. *oubling the size of the (resultant) force doubles the acceleration. The mass An object will accelerate in the direction of the resultant force. A force on a large mass will accelerate it less than the same force on a smaller mass. *oubling the mass halves the acceleration.
+ere is an euation relating acceleration to force and mass: #orce $ mass % acceleration "orce is measured in newtons, %
-ass is measured in ilograms, g Acceleration is measured in metres !er second suared, ms /.
#alling objects You should be able to describe the forces affecting a falling object at different stages of its fall. 0sually, you need to thin about two forces: 1.
The weight of the object. This is a force acting downwards, caused by the object1s mass in the 2arth1s gravitational field.
Air resistance. This is a frictional force acting in the o!!osite direction to the movement of the object.
Three stages of falling When an object is dro!!ed, we can identify three stages before it hits the ground: 3.
At the start, the object accelerates downwards because of its weight. There is no air resistance. There is a resultant force acting downwards. /. As it gains s!eed, the object1s weight stays the same, but the air resistance on it increases. There is a resultant force acting downwards. 2ventually, the object1s weight is balanced by the air resistance. 3. There is no resultant force and the object reaches a steady s!eed, called the terminal velocity. Terminal velocity What ha!!ens if you dro! a feather and a coin together4 The feather and the coin have roughly the same surface area, so when they begin to fall they have about the same air resistance. As the feather falls, its air resistance increases until it soon balances the weight of the feather. The feather now falls at its terminal velocity. 5ut the coin is much heavier, so it has to travel uite fast before air resistance is large enough to balance its weight. In fact, it !robably hits the ground before it reaches its terminal velocity. &n the oon An astronaut on the -oon carried out a famous e#!eriment. +e dro!!ed a hammer and a feather at the same time and found that they landed together. The -oon1s gravity is too wea for it to hold onto an atmos!here, so there is no air resistance. When the hammer and feather were dro!!ed, they fell together with the same acceleration.
Circular Motion & Centripetal Force
From Newton’s first law of motion it is known that an object will remain stationary, or keep moving at constant velocity in a straight line unless acted upon by an unbalanced force !hen an object moves in a circular path its direction is changing all the time therefore according to Newton’s first law there must be an unbalanced force acting upon it all the time !hen an object moves in a circle although its speed is constant the direction is continuously changing "herefore its velocity is continuously changing as velocity is speed in a particular direction "he changing velocity in time means the object is accelerating all the time
"he resultant force which causes this acceleration is the centripetal force The centripetal force always acts toward the centre of the circle. "he centripetal force is determined from the following e#uation$
%f a ball is tied to the end of a strong string and swung in a circle, the ball accelerates towards the centre of the circle "he centripetal force which causes the inwards acceleration is from the tension in the string caused by the person’s hand pulling the string %f the string breaks there is no longer a resultant force acting on the ball, so it will continue its motion in a straight line at constant speed
"he centripetal force re#uired to make an object perform circular motion increases in the following cases$
%f the mass of the object increases
%f the velocity of the object increases
%f the radius of the circle decreases
"he above points are evident when considering the e#uation for centripetal force