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# Potential energy and conservation of Energy

الكلية كلية التربية للعلوم الصرفة     القسم قسم الفيزياء     المرحلة 1
أستاذ المادة فؤاد عطية مجيد       29/05/2018 09:19:53
Example (5): When two objects of unequal mass are hung vertically over a frictionless pulley of negligible mass, as shown in Fig (a), the arrangement is called an Atwood machine. The device is sometimes used in the laboratory to measure the freefall acceleration. Determine the magnitude of the acceleration of the two objects and the tension in the lightweight cord.
Solution: When the Newton’s 2nd law is applied to object 1, we obtain
???F_y=T-m_1 g=m_1 a_1 (1)?
Similarly, for object 2 we find
???F_y=m_2 g-T=m_2 a_2 (2)?
When (2) is added to (1), T drops out and we get
-m_1 g+m_2 g=m_1 a_1+m_2 a_2
When (3) is substituted into (1), we obtain
a_y=((m_2-m_1)/(m_1+m_2 ))g (3)
T=((2m_1 m_2)/(m_1+m_2 ))g (4)

Work and Energy
6.1 Work and Energy
In this section we will see how to relate force particle motion in a second way. The scalar produced of force and displacement defines work. The product of mass and the square of a particle’s velocity gives twice the kinetic energy. Combining work and kinetic energy we drive the work-energy principle. This principle plays a role which is analogous to hat of Newton’s second law.
Energy is the capacity that an object has for preforming work.
Kinetic energy is energy an object possesses because of its motion
Work is energy transferred to or form an object via force acting on the object

6.3 Variable Force / Work
Force is a function of position, spring, gravity, etc. The total work done on the particle when moving from x_i to x_f is the sum of all the work done during successive infinitesimal displacement, that is
W=lim?(?x?0)????F_x (x_i)?x?
W=?_(x_i)^(x_f)??F_x dx? [definite integral]
Work? area bounded by the curve F_x (x)
Example Spring Force:
F=-kx
How much work is needed to move a spring (fixed at one end) from x=a to
x=b?

W=?_a^b?F_x dx
=?_a^b??(-kx)dx=? (-kx^2)/2?|_a^b ?=-k/2(b^2-a^2)
Work in Three Dimension (3-D)
In general:
W=F ?.?r
F ? : constant force
?r : displacement

المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .