Question

a 4.0-kg block is moving at 5.0 m/s along a horizontal frictionless surface toward an ideal spring that is attached to a wall. After the block collides with the spring, the spring is compressed a maximum distance of 0.68 m. ) Suppose now friction is present and k = 0.10 but only acts while the block is actually compressing the spring. What is the speed at one-half of the maximum distance the block when friction is present?

Answer 1

energy in KE=spring energy+friction energy
wo/friction: 1/2 m*25=1/2 k .68^2 solve for spring constant k.

w/friction
first find the max distance of compression.
1/2 m 25=1/2 k xmax^2+.1mg*xmax

solve for x max, note it is a quadratic.

now, the hard part..speed when at the half way point.
KE at half way=initialKE-PE+frictionloss
1/2 vh^2=1/2 m 25 -1/2 k (xmax/2)^2 -.1mg(xmsz/2)

solve for vhalf

Answer 2

i did not get this . can u do little bit calculations too.