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Block moves over smooth and rough surface into a spring, find max dist spring is compressed. Also kinetic energy and centripetal accel?
I have no idea how to do problem #3. I'm currently working on the next two which look pretty easy but I still want to check to make sure I'm getting the correct answers (since no answer key). I'm studying for an exam for tomorrow.
(Also your help was much appreciated, NCS, with my previous question in case you help me again.)
1 Answer
- TechnobuffLv 77 years agoFavorite Answer
Take 'smooth' as being frictionless.
PE of mass before descending = (mgh) = (8 x 9.8 x 20) = 1,568 Joules. This converts to KE as it slides down.
V reaching the bottom = sqrt.(2KE/m) = sqrt.(3,136/8) = 19.8m/sec.
The rough area is 5 metres long, with a µK of 0.4.
Braking force = (8 x g) x 0.4 = 31.36N.
Acceleration = (f/m) = 31.36/8 = -3.92m/sec^2.
Change in V over 5 metres = sqrt.(2ad) = 6.261m/sec.
V at spring = (19.8 - 6.261) = 13.54m/sec.
KE = 1/2 (mv^2) = 733.33 Joules.
The spring constant is 4,000N/m.
Compression distance = (733.33/4,000) = 0.183 metre, or 18.3cm.