A block of mass m=2 kg on a horizontal surface is connected to a spring connected to a wall (see figure). The spring has a spring constant k= 12 N/m. The static friction coefficient between the block and the surface is μs= 0.5 , and the kinetic friction coefficient is μk= 0.2 . Use g=10 m/s2 for the gravitational acceleration.
a) The spring is initially uncompressed and the block is at position x=0. What is the minimum distance x1 we have to compress the spring for the block to start moving when released? (in meters)
b)Find the distance |x2−x1| between the point of release x1 found in (a), and the point x2 where the block will come to a stop again. (in meters)
c)What time t12 does it take the block to come to a rest after the release? (i.e., the time of travel between points x1 and x2; in seconds)
d)What will happen after the block has come to a rest at point x2?
i)The block will move back towards x1, and it will oscillate with constant frequency and exponentially decreasing amplitude.
ii)The block will move back towards x1, and it will oscillate while decreasing both frequency and amplitude.
iii) The block will start moving back towards x1, and it will come to a final halt before reaching it.
iv) The block will stay at its resting position x2
v) The answer depends on whether x2>0 or x2<0.
A)mus*m*g=k*x
B)delta x= 2*muk*m*g/k+2*mus*m*g/k
C)resolve second equation differential