APPLICATIONS OF NEWTON'S LAWS - I
1. The conclusion from F = ma is that if F = 0 then a = 0 ! quite easy! yet how powerful ! This says that for anybody which is not accelerating the sum of all the forces acting upon it should vanish.
2. Examples of systems which is in equilibrium: a stone lying on the ground; a pencil balanced on your finger; an aircraft flying at a constant speed, a ladder placed against the wall, and constant height.
3. Examples of systems out of equilibrium: a plane diving downwards; a stone thrown upwards that is at its highest point; a car at rest whose driver has just stepped on the car's accelerator.
4. If you know that the acceleration of a body, it is simple to find the force which causes it to accelerate. Example: An aircraft of mass m has position vector,
What force is acting upon it?
SOLUTION:
6. Ropes are quite useful because you can pull from the distance and can change the direction of the force. The tension, commonly denoted by T , is the force which you would feel if you cut the rope and then grabbed the ends. For a mass less rope the tension remains the same at every point along the rope. Because, if you take any small piece of the rope it weighs very less. So if the force on one side of the rope was any different from the force on the other side, it would be accelerating quite more. All this was for the "ideal rope" condition which has no mass and never breaks.
7. We are well-known about the frictional force. When the two bodies are rubbed against each other, the frictional force acts upon each body separately in the opposite direction of the motion
(that is, it acts to slow down the motion). The harder you press the two bodies against each
G G G
other, the greater the friction. Mathematically, F = μ N , where N is the force by which you press the two bodies against each
other .The quantity μ is called the coefficient of friction. It is quite large for the rough surfaces, and less for smooth ones. Remember that G G
F = μ N is an empirical relation and holds only approximately.
This is certainly true: if you put a large mass on the table, the table it will start to bend and will eventually break.
8. Friction is caused due to the roughness at the microscopic level
- if you glance at any surface with the powerful microscope
you will observe unevenness and jaggedness. If these big bumps are levelled, friction still will not disappear because there will be little bumps due to the atoms. More accurately, atoms from the two bodies will interact with each other because of the electrostatic interaction between their charges. Even when the atom is neutral, even though it can still exchange electrons and there will be a force because of the surrounding atoms.
9. Suppose that the two blocks below are on the frictionless surface:
Hear find out the tension and acceleration: The total force on first mass is F - T and so F - T = m1a. Thus the force on the second mass is simply T and so T = m2 a.
Solving the above, we get:
10. There is a usual principle by using which you may solve the equilibrium problems. For equilibrium, the sum of the forces in every direction should vanish. So Fx = Fy = Fz = 0. You may always decide the x, y, z directions according to your convenience. So, for instance, as in the lecture problem dealing with the body sliding down an inclined plane, you can choose the directions to be along and perpendicular to surface of the plane.