Block of mass \"m\" rests on an incline which makes an angle(theta) with the hor
ID: 1915473 • Letter: B
Question
Block of mass "m" rests on an incline which makes an angle(theta) with the horizontal, the coefficients of static and kinetic friction is given, the block is attached to a massless spring with a spring constant k. The relaxed length of the spring is L.
A) The block is pulled until the length is L+x, what is the maximum extension (X_max) of the spring for which the block will remain stationary when released?
B) At t=0 when the extension is (X_max) the block is gently touched and starts moving up, as the block moves the spring gets shorter. At some point in time(still getting shorter) the extension is x,
What is the work done by gravity & by the spring force?
**please help explain and show work very clearly on how to get to answer, to understand**
No picture given, but can be drawn or imagined pretty easily
willl be rated lifesaver
Explanation / Answer
Let the coefficient of static friction be
(A)so writing all the force parallel to the slope
mgcos + mgsin = kX_max
X_max=(mgcos + mgsin)/k
(B) when the extension is x, the distance it moved vertically up = (X_max-x)sin
so work done by gravity = mgh= mg(X_max-x)sin
work done by spring= 0.5k(1/X_max2-1/x2)