Question

Work Done by the Govtational Force bute the gravitational force G m./r into the integral equation on the previous genith Y replacing and find the work done by this force df w is the work done by the gravitational for moves away from t he gravitational force positive, negative, or zero when an object in the Earth? When it moves toward the Earth? When it orbits the Earth in a circle? Part B: Conservative and Non-conservative Forces welop and understorence between whether that Discussion The goal here is to develop and understand the Law of Conservation of Energy. The first step in doing this is to understand the difference between conservative and non- conservative forces. The nature of the work done by a force determines whether that force is conservative or non-conservative. The work done by weight, the elastic force, and kinetic friction will be considered here. A force is defined as a conservative force if the work done by such a force on an object moving between two points does not depend on the path taken between these two points. For example, consider the object shown to the left on the following page as it moves between points A and B. The work done by a force when taking any of the paths shown will be identical if the force acting on the object is conservative. Conversely, a non- conservative force produces a path-dependent value for work. Each path taken between points A and B will require a different amount of work from a non-conservative force. There is another more practical method of identifying conservative forces. Consider an object moved from point A to point B and then back to point A, as shown to the right on the following page. The object can be moved along any path in either direction. If the force is conservative, the work done from A to B will simply be the negative of the work done from B to A. Thus, the net work done by a conservative force along any closed path is zero. Likewise, the work done by a non-conservative force along such a closed path will be nonzero.

Answer 1

WORK done by Gravitational force- moving a displacement th Fy displacement When object is moving up then direction of gravitational force is downward lathile Il displacement is upward ie angle between force and displacement is 180 so work done by grauitational force - - I W = f Eids - 5 C - fg ds), - - f Eds D2 z So work done is negative When object is moving down then due granita- tional force and displacement both are in the same direction (o=0°) so work done - - W = Foods =) = Fg ds Coso = J F ds So work done is tve. Direction of when body moves in motion I circular motion around the earth the for every point of motion direction os displacement is berpendit cular to gravitational force So wore done by gravity- W = = F D Foods - Rods Cosgo d o

force- Conseаvative and Non-Conservative @ W= mg (S, -S.) 10 1 Wang (S, -S2) - = - ing CS2-S1) Net work done- C het = W, +W2 = ing (S-5,) - ing CS-S) @ yes, weight is a Conseаvative force because work done by weight only depends upon initial and final position of body and not on the bath followed by body Elastic force- @ work done by clastic, Force when object is moon I moved from s to S2 - - W, = 2 ks - 1 ks? - W = b k ( -8) 6 work done by elastic force when object is moved from sto s back - W₂ = £ Rs ² - 1 ks = W2 = - 1 R (-) © Net Work-done- - Ilmet = W, +W₂ = 1 k 15-8?) - 1 R (8-8) » Whet = 0 mo0o0 -

a Yes, spring force (Elastic Force) is a conser- Native force because work done by this force depends only upon drittial and final Position of body. Kinetic fluction 14 X (kinetic friction) @ work the object done by kinetic from 8 to 82- friction to move 6 work done by kinetic friction to move the object from se to s, - The = tkx8 o Net work done- What a W, W2 = -fR XS FRX8 lahet = -2fR8 @ Kinetic friction is not a conservative force because it depends upon the bath followed by object also coordone by kmetic friction or work against Kinette Poletion does not merease stored in the form of potential energy of object -