Aman Bansal
Last Activity: 11 Years ago
Dear Student,
In this problem, you will use your prior knowledge to derive one ofthe most important relationships in mechanics: the work-energytheorem. We will start with a special case: a particle of mass
moving in the
x direction at constant acceleration
.During a certain interval of time, the particle accelerates from
to
, undergoing displacement
given by
.
part A.
Find the acceleration
of the particle.
Express the acceleration in terms of
,
, and
.
part B
Find the net force
acting on the particle.
Express your answer in terms of
and
.
part c
Find the net work
done on the particle by the external forces during the particle''smotion.
Express your answer in terms of
and
.
part D
Substitute for
from Part B in the expression for work from Part C. Then substitutefor
from the relation in Part A. This will yield an expression for thenet work
done on the particle by the external forces during the particle''smotion in terms of mass and the initial and final velocities. Givean expression for the work
in terms of those quantities.
Express your answer in terms of
,
, and
.
part E
Find the net work
done on the particle by the external forces during the motion ofthe particle in terms of the initial and final kineticenergies.
Express your answer in terms of
and
.
part F
Evaluate the integral
.
Express your answer in terms of
,
, and
.
part G
A particle moving in the
x directionis being acted upon by a net force
, for some constant
.The particle moves from
to
. What is
, the change in kinetic energy of the particle during thattime?
Express your answer in terms of
and
.
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Thanks
Aman Bansal
Askiitian Expert
