Springs A very common problem with a variable force is a spring L F △x In this spring, the force gets greater as the spring is further compressed Hooks Law k△x Active Figure AX is the amount the spring is stretched or compressed from it resting position Physics 121: Lecture 13, Pg 6
Physics 121: Lecture 13, Pg 6 Springs A very common problem with a variable force is a spring. In this spring, the force gets greater as the spring is further compressed. Hook’s Law, FS = - k x x is the amount the spring is stretched or compressed from it resting position. F x Active Figure
1-D Variable Force Example: Spring For a spring we know that Fx=-kx(Hook's law) F(×) X relaxed position WA F=-k F=-k Physics 121: Lecture 13, Pg 7
Physics 121: Lecture 13, Pg 7 1-D Variable Force Example: Spring For a spring we know that Fx = -kx (Hook’s law). F(x) x2 x x1 -kx relaxed position F = - k x1 F = - k x2
Spring… The work done by the spring Ws during a displacement from X, to x2 is the area under the F(x)vs x plot between x and x F(×) 1 X relaxed position WA Physics 121: Lecture 13, Pg 8
Physics 121: Lecture 13, Pg 8 Spring... The work done by the spring Ws during a displacement from x1 to x2 is the area under the F(x) vs x plot between x1 and x2 . Ws F(x) x2 x x1 -kx relaxed position
Spring The work done by the spring Ws during a displacement from x, to x, is the area under the F(x)vs x plot between X, and x2 F(×) Ws=-1/2[(kx2)(x2)-(kx1)(x1)] kX Physics 121: Lecture 13, Pg 9
Physics 121: Lecture 13, Pg 9 Spring... The work done by the spring Ws during a displacement from x1 to x2 is the area under the F(x) vs x plot between x1 and x2 . x1 x2 F(x) x Ws kx1 kx2 -kx Ws Ws = - 1/2 [ ( kx2 ) (x2 ) - (kx1 ) (x1 ) ]
Lecture 13. AcT 1 Work Energy a box sliding on a horizontal frictionless surface runs into a fixed spring, compressing it a distance x from its relaxed position while momentarily coming to rest If the initial speed of the box were doubled and its mass were halved, how far x would the spring compress? (b)x=√2x(c)x=2X Physics 121: Lecture 13, Pg 10
Physics 121: Lecture 13, Pg 10 Lecture 13, ACT 1 Work & Energy A box sliding on a horizontal frictionless surface runs into a fixed spring, compressing it a distance x from its relaxed position while momentarily coming to rest. If the initial speed of the box were doubled and its mass were halved, how far x’ would the spring compress ? x (a) x' = x (b) x' = 2 x (c) x' = 2 x