Problem: Spring pulls on mass A spring(constant k) is stretched a distance d, and a mass m is hooked to its end. The mass is released (from rest. What is the speed of the mass when it returns to the relaxed position if it slides without friction? relaxed position /园 after release back at relaxed position Physics 121: Lecture 13, Pg 11
Physics 121: Lecture 13, Pg 11 Problem: Spring pulls on mass. A spring (constant k) is stretched a distance d, and a mass m is hooked to its end. The mass is released (from rest). What is the speed of the mass when it returns to the relaxed position if it slides without friction? relaxed position stretched position (at rest) d after release back at relaxed position vr v m m m m
Problem: Spring pulls on mass First find the net work done on the mass during the motion from x= d to x o(only due to the spring) m stretched position(at rest) LM园 relaxed position Physics 121: Lecture 13, Pg 12
Physics 121: Lecture 13, Pg 12 Problem: Spring pulls on mass. First find the net work done on the mass during the motion from x= d to x= 0 (only due to the spring): stretched position (at rest) d relaxed position vr m m i
Problem: Spring pulls on mass Now find the change in kinetic energy of the mass m stretched position(at rest) LM园 relaxed position Physics 121: Lecture 13, Pg 13
Physics 121: Lecture 13, Pg 13 Problem: Spring pulls on mass. Now find the change in kinetic energy of the mass: stretched position (at rest) d relaxed position vr m m i
Problem: Spring pulls on mass. Now use work kinetic-energy theorem: W=△KE m m stretched position(at rest) LM园 relaxed position Physics 121: Lecture 13, Pg 14
Physics 121: Lecture 13, Pg 14 Problem: Spring pulls on mass. Now use work kinetic-energy theorem: Wnet = WS = KE. stretched position (at rest) d relaxed position vr m m i 1 2 2 kd = 2 mvr 2 1 m k vr = d
Problem: Spring pulls on mass Now suppose there is a coefficient of friction u between the block and the floor The total work done on the block is now the sum of the work done by the spring Ws(same as before)and the work done by friction Wf W=fAr=-u mg d △r m stretched position(at rest) d LA园(= mg relaxed position Physics 121: Lecture 13, Pg 15
Physics 121: Lecture 13, Pg 15 Problem: Spring pulls on mass. Now suppose there is a coefficient of friction between the block and the floor The total work done on the block is now the sum of the work done by the spring WS (same as before) and the work done by friction Wf . Wf = f. r = - mg d stretched position (at rest) d relaxed position vr m m i f = mg r