A spring (R) of a horizontal axis, of negligible mass, of unjoint turns and of stiffness k= 40 N/m, is fixed, 0000000000 by one of its extremities to a support. The spring's other extremity is free at a point 0 [figure (a)]. Figure (a) We displace the free extremity of the spring along its axis from the point O to the point A by distance x = 10 cm. We place in front of the spring a (S) of mass m=250 g [figure (b)]. A At t = 0, we release (S) without initial speed. (S) moves without friction between A and O. Figure (b) At the instant t the solid passes by O and leaves the spring with a speced Vo. When (S) passes by O it is subjected to a force of friction, supposed constant, and then stops at a point M such that OM=20 cm. %3D The zero reference of gravitational potential energy is taken to be the horizontal plane passing through the axis of the spring. 1) Calculate the variation of the mechanical energy of the system [Earth ; (S) ; (R)] when (S) passes from A to M. 2) Deduce the magnitude f of the force of friction. 3) Calculate the speed V. 4) Represent the graph of the mechanical energy of the system [Earth ; (S) ; (R)] as a function of the distance d between A and

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A spring (R) of a horizontal axis, of negligible mass,
of unjoint turns and of stiffness k = 40 N/m is fixed,
by one of its extremities to a support. The spring's
other extremity is free at a point O [figure (a)].
000000000
Figure (a)
We displace the free extremity of the spring along its
axis from the point O to the point A by distance
x = 10 cm. We place in front of the spring a (S) of
mass m=250 g [figure (b)].
(S)
M
A
At t = 0, we release (S) without initial speed. (S)
moves without friction between A and O.
Figure (b)
At the instant t the solid passes by O and leaves the spring with a spced Vo. When (S) passes by O it is
subjected to a force of friction, supposed constant, and then stops at a point M such that OM = 20 cm.
The zero reference of gravitational potential energy is taken to be the horizontal plane passing through
the axis of the spring.
1) Calculate the variation of the mechanical energy of the system [Earth ; (S) ; (R)] when (S) passes
from A to M.
2) Deduce the magnitude f of the force of friction.
3) Calculate the speed Vo.
4) Represent the graph of the mechanical energy of the system [Earth ; (S) ; (R)] as a function of the
distance d between A and
Transcribed Image Text:A spring (R) of a horizontal axis, of negligible mass, of unjoint turns and of stiffness k = 40 N/m is fixed, by one of its extremities to a support. The spring's other extremity is free at a point O [figure (a)]. 000000000 Figure (a) We displace the free extremity of the spring along its axis from the point O to the point A by distance x = 10 cm. We place in front of the spring a (S) of mass m=250 g [figure (b)]. (S) M A At t = 0, we release (S) without initial speed. (S) moves without friction between A and O. Figure (b) At the instant t the solid passes by O and leaves the spring with a spced Vo. When (S) passes by O it is subjected to a force of friction, supposed constant, and then stops at a point M such that OM = 20 cm. The zero reference of gravitational potential energy is taken to be the horizontal plane passing through the axis of the spring. 1) Calculate the variation of the mechanical energy of the system [Earth ; (S) ; (R)] when (S) passes from A to M. 2) Deduce the magnitude f of the force of friction. 3) Calculate the speed Vo. 4) Represent the graph of the mechanical energy of the system [Earth ; (S) ; (R)] as a function of the distance d between A and
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