Question

Two children stretch a jump rope between them and send wave pulses back and forth on it. The rope is 4.5 m long, its mass is 0.42 kg, and the force exerted on it by the children is 71 N. (a) What is the linear mass density of the rope (in kg/m)?

(b) What is the speed of the waves on the rope (in m/s)?

Answer 1

The linear mass density of the rope is 0.0933 kg/m and the speed of the waves on the rope is 34.65 m/s.

Step-by-step explanation:

To calculate the linear mass density of the rope, we use the formula μ = m/L, where m is the mass of the rope and L is the length of the rope. In this case, the linear mass density is 0.42 kg / 4.5 m = 0.0933 kg/m.

To calculate the speed of the waves on the rope, we use the formula v = √(F/μ), where F is the force exerted on the rope and μ is the linear mass density. In this case, the speed of the waves is √(71 N / 0.0933 kg/m) = 34.65 m/s.

Answer 2

density = 0.0933 kg/m

speed = 27.581 m/s

Step-by-step explanation:

given data

length L = 4.5 m

mass m = 0.42 kg

force F = 71 N

to find out

mass density and speed

solution

we find linear mass density

linear mass density = mass / length

put here all value

density = 0.42 / 4.5

density = 0.0933 kg/m

and

speed of wave

speed = √(F/density)

speed = √(0.42/0.933)

speed = 27.581 m/s