Consider the following hypotheses: 12:V ) >(x)) Use rules of inference to prove that the following conclusion follows from th
ese hypotheses: Clearly label the inference rules used at every step of your proof 2. Consider the following hypotheses: H1 Vr (C()--A(x)) H2 : Vr (A() Vy B(y)) Use rules of inference to prove that the following conclusion follows C: 3r (B(x) AC()) H3: Br A(a) from these hypotheses: Clearly label the inference rules used at every step of your proof. 3. Consider the following predicate quantified formula: r y (P(x, y)P(, y)) Prove the unsatisfiability of this formula using rules of inference.
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The work done to pull the sister back on the swing is equal to the increase in potential energy of the sister:
(1)
where m is the sister's mass, g is the gravitational acceleration and
is the increase in altitude of the sister with respect to its initial position.
By calling
the angle of the chain with respect to the vertical, the increase in altitude is given by
(2)
where L is the length of the chain.
Putting (2) inside (1), we find
from which we can find the mass of the sister:
where m is the sister's mass, g is the gravitational acceleration and
By calling
where L is the length of the chain.
Putting (2) inside (1), we find
from which we can find the mass of the sister:
AS
work done =W = F.d = F d cosФ (Ф is angle between force F and displacement d) If a body/object is moving on a smooth surface (friction-less surface ) .There is no force acting on that body. F=0 so W=FdcosФ= (0)dcosФ ⇒ W=0
Now if a body is facing some amount of force but under the action of force there is no displacement covered. d=0 so W =FdcosФ= F(0)cosФ ⇒W=0
example: A person is applying a force on rigid wall but wall remains at rest there is no displacement occurs in wall.
The third term upon which work done dependent is angle between force and displacement i.e Ф. If Ф=90° then W= FdcosФ= Fdcos90⇒ W=0 ( as cos 90°=0)
