A100 meter rope is 20 kg and is stretched with a tension of 20 newtons. if one end of the rope is vibrated with small amplitude at 10hz, what would the velocity of waves traveling down it be? what would the velocity be if it rained and the rope soaked up 5 kg of water?

The velocity waves before rain is 10 m/s

The velocity of wave after the rope soaked up 5 kg more is 8.944 m/s

Solution:

As per the question:

Length of the rope, l = 100 m

Mass of the rope, m = 20 kg

Force due to tension in the rope,

Frequency of vibration in the rope, f = 10 Hz

Extra mass of the rope after being soaked in rain water, m' = 5 kg

Now,

In a rope, the wave velocity is given by:

        (1)

where

= mass density

Mass density before soaking,

Mass density after being soaked,

Initially, the velocity is given by using eqn (1):

The velocity after being soaked in rain:

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards