Question

A child of mass 26 kg swings (摇摆) at the end of an elastic cord (弹性绳). At the bottom of the swing, the child’s velocity is horizontal, and the speed is 8 m/s. At this instant the cord is 3.10 m long. [You can neglect air resistance.] (a)At this instant, what is the parallel component of the rate of change of the child’s momentum? (b)At this instant, what is the perpendicular component of the rate of change of the child’s momentum? (c)At this instant, what is the net force acting on the child? (Use the Momentum Principle.) (d)What is the magnitude of the force that the elastic cord exerts on the child? (It helps to draw a force diagram.) (e)The relaxed length of the elastic cord is 3.06 m. What is the stiffness of the cord?

Answer 1

a)

the parallel component of the rate of change of the child’s momentum is

F_parallel =0

In vector form <0,0,0> N

b)

the perpendicular component of the rate of change of the child’s momentum

F_{perpendicular}=mV²/r =26*8²/3.1 = 536.77 N

in Vector form is

<0,536.77,0> N

c)

the net force acting on the child

F_net =F_{perpendicular} =536.77 N

in Vector form is

<0,536.77,0> N

d)

the magnitude of the force that the elastic cord exerts on the child

F=536.77+26*9.81 =791.83 N

e)

the stiffness of the cord

K=F/(x-x_o)=791.83/(3.1-3.06)

K=19795.85 N/m