Answer to Question #246677 in Physics for Jordan

Question

Two children stretch a jump rope between them and send wave like sea back and forth. The rope is 4.3 meters long, it’s mass is 0.58kg, and the force exerted by the children is 31 N. What is the linear mass density of the rope? (Kg/m)? What is the speed of the waves on the rope? (M/s)?

Answer 1

(a) We can find the linear mass density as follows:

$$\mu = \dfrac{m}{L}=\dfrac{0.58\ kg}{4.3\ m}=0.13\ \dfrac{kg}{m}.$$

(b) We can find the speed of the waves on the rope as follows:

$$v=\sqrt{\dfrac{T}{\mu}}=\sqrt{\dfrac{31\ N}{0.13\ \dfrac{kg}{m}}}=15.4\ \dfrac{m}{s}.$$