A 10.0 kg block is released from point A with initial speed of 1m/s (it is given
ID: 1973435 • Letter: A
Question
A 10.0 kg block is released from point A with initial speed of 1m/s (it is given a push) in the figure below. The track is frictionless except for the portion between points B and C, which has a length of 6.00 m. The block travels down the track, hits a spring of force constant 2200 N/m, and compresses the spring to 0.350 m from its equilibrium position before coming to rest momentarily. Determine the coefficient of kinetic friction between the block and the rough surface between B and C.Figure:
http://www.solutioninn.com/images/P-M-P-E%20(57).PNG
Explanation / Answer
well, you can solve this problem using the conservation of mechanic energy:
lets imagine a reference level, on the floor, i´ll use gravity g=9.81 m/s2
at point "A", the mechanic energy of all system:
Ea= mva2/2 + mgha +kxa2/2
Ea=10Kg(1ms-2)2/2+(10Kg)(9.81m/s2)(3m)+0=299.3 J
Then the block, slides; passes trough the track, the non-frictionless part BC. and reaches the spring. ['coming to rest momentarily']; so at the point, the energy:
E=mv2/2 + mgh +kx2/2
E=0+0+(2200 N/m)(0.350 m)2/2 [since it's resting V=0, & its on the refernce level]
E=134.75 J
What happened? if at the star the system (block+spring) had 299.3 J of energy and at the end of the track (when the block reaches the spring and rests momentarily) has 134.75 J; the loss of energy is due the friction (between) the points B & C:
This means that the friction worked against the moving:
Ea-E=Wfriction=mg(d) [this is the work during the distance d=6m]
299.3 J - 134.75 J = (10Kg)(9.81m/s2)(6m)
=0.27956 0.28 [using g=9.81 m/s2]
*The principle of conservation of the mechanic energy, is applicable considering that when a force like friction appears, it'll work.
If you know all the data between points 1 & 2, you can directly use:
E2-E1=Wf [since E2<E1, you need to consider that the friction work is negative-its against the movement]
(mv22/2 + mgh2 +kx22/2)-(mv12/2 + mgh1 +kx12/2)=Wf [Wf=-mgd]
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