Block B is now removed, so that the right end of the spring is now directly in c
ID: 1358442 • Letter: B
Question
Block B is now removed, so that the right end of the spring is now directly in contact with the wall, as shown. During the interval from t_3 to t_4, block A is again pushed a distance d_A by a hand exerting a constant force F_A. The wall exerts a force on the spring that varies with time but is always directed to the left. Consider the interval from t_3 to t_4: Let system Y consist of block A and the spring. Would you expect the net work on system Y by external forces during this interval to be greater than, less than, or equal to the net work by external forces on system X between t_1 and t_2? Explain. Write an expression for the work done on block A by the hand during this interval in terms of the given quantities. Explain. What is the displacement of the left end of the spring during this interval? What is the displacement of the right end of the spring during this interval? Which of these displacements should be used to calculate the work done on the spring by the wall? Explain. Is the work on the spring by the wall positive, negative, or zero? Write an expression for the net work done on system Y by external, forces in terms of the given quantities. Explain. Is your answer for question b.iv consistent with your answers for questions b.i and a.iii? If it is consistent, explain how. If it is not consistent, resolve the inconsistency.Explanation / Answer
here,
Considering forces as:
to right = positive
to left = negative
overall there are three forces acting on system mainly;
F = force applied by hand on block A = +F
Fw = force applied by wall on spring = -Fw
Fx = force applied by spring on block = -Fx
1.)
writing Eqn for net force we have
Fnet = 0
t = 4
Fa - Fx -Fw = 0
Fa = Fx -Fw
Fa = -kdA - Fw ------------------(1)
2.)
as Work Done = Force * displacement * cosA
As force is perpendicular to displacement CosA = o degrees
W = Fa.da
W = (-kdA - Fw )*dA
3.)
Displacement for leftend of spring = dA
as spring is fixed to wall so there will no displacement for right end of spring
as the wall is no moving, so work done by wall on spring will be zero but it will apply equal and opposite force on spring as Newton third la state.
4.)
as ,
W = Fa.da
so,from Eqn 1 we get,
W = (-kdA - Fw )*dA