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Lecture 5 Examples Hook’s Law Simple Pendulu m Work and Energy Power. Example 9:.
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Lecture 5ExamplesHook’s LawSimple Pendulum Work and Energy Power
Example 9: A traffic light weighing 122 N hangs from a cable tied to two other cables fastened to a support, as in this Figure. The upper cables make angles of 37.0° and 53.0° with the horizontal. These upper cables are not as strong as the vertical cable, and will break if the tension in them exceeds 100 N. Will the traffic light remain hanging in this situation, or will one of the cables break?
Example 10: A ball of mass m1 and a block of mass m2 are attached by lightweight cord that passes over a frictionless pulley of negligible mass, as in this Figure. The block lies on a frictionless incline of angle ɵ . Find the magnitude of the acceleration of the two objects and the tension in the cord.
1.9 HOOKE’S LAW • Periodic motion, from masses on springs to vibrations of atoms, is one of the most important kinds of physical behavior. • Hooke’s law: where the force is proportional to the displacement, tending to restore objects to some equilibrium position. A large number of physical systems can be successfully modeled with this simple idea, including the vibrations of strings, the swinging of a pendulum, and the propagation of waves of all kinds. All these physical phenomena involve periodic motion.
If the spring is stretched or compressed a small distance x from its unstretched or equilibrium position and then released, it exerts a force on the object as shown in this Figure From experiment this spring force is found to obey the equation: where x is the displacement of the object from its equilibrium position (x =0) and k is a positive constant called the spring constant.
This force law for springs was discovered by Robert Hooke in 1678 and is known as Hooke’s law. The value of k is a measure of the stiffness of the spring. Stiff springs have large k values, and soft springs have small k values.
The force exerted by a spring on an object varies with the displacement of the object from the equilibrium position, x = 0. (a) When x is positive (the spring is stretched), the spring force is to the left. (b) When x is zero (the spring is unstretched), the spring force is zero. (c) When x is negative (the spring is compressed), the spring force is to the right.
Example 11: A common technique used to measure the force constant of a spring is demonstrated by the setup in this Figure. The spring is hung vertically, and an object of mass m is attached to its lower end. Under the action of the “load” mg, the spring stretches a distance d from its equilibrium position. (A) If a spring is stretched 2.0 cm by a suspended object having a mass of 0.55 kg, what is the force constant of the spring?
MOTION OF A PENDULUM A simple pendulum is another mechanical system that exhibits periodic motion. It consists of a small bob of mass m suspended by a light string of length L fixed at its upper end, as in this Figure. When released, the bob swings to and fro over the same path.
The pendulum bob moves along a circular arc, rather than back and forth in a straight line. When the oscillations are small, however, the motion of the bob is nearly straight, so Hooke’s law may apply approximately. In the last Figure, d is the displacement of the bob from equilibrium along the arc. Hooke’s law is F = - k x, so we are looking for a similar expression involving s, Ft = - k s, where Ftis the force acting in a direction tangent to the circular arc.
From the figure, the restoring force is • Where ω is the angular frequency, f is frequency, T is the period.
1.10 Work and Energy What do we need to move? E N E R G Y Where do we get this energy from? F O O D
In fact ….. NOTHING would happen without ENERGY
What is Work and What Isn’t? • Doing homework isn’t work. • Carrying somebody a box isn’t work… • Carrying somebody a box and he is walking is work—in fact, about one unit of work.
Work is only done by a force… and, the force has to move something! • Suppose I lift one kilogram up one meter… I do it at a slow steady speed—my force just balances its weight, let’s say 10 Newton. • Definition: if I push with 1 Newton through 1 meter, I do work 1 Joule. So lifting that kilogram took 10 Joules of work.
WORK : The work done by the force is defined to be the product of component of the force in the direction of the displacement and the magnitude of this displacement. Thus : W= F d cosθ
1.11 POWER POWER:- The rate of doing work is called as power. or The rate at which work is done is called as power. Like work and energy, power is a scalar quantity.
Average and instantaneous power When a quantity of work is done during a time interval , the average work done per unit time or average power is defined to be We can define the instantaneous power as the limiting value of the average power as approaches to zero. M.K.S System joule/sec (or) kg m2 s-3 (or) watt.
Alternative FORMULAE FOR POWER Thus the power associated with force F is given by P = F .v where v is the velocity of the object on which the force acts. Thus P = F . v = F v cos θ
References • Physics for scientists and engineers with modern physics. (Serway, Jewett) • Physics by Kane and Sternhiem. • Physics ,Walker, James S. • http://www.worldofteaching.com/Please visit and I hope it will help you.
