A rope of length L = 5.2 m with a total mass of m = 0.275 kg is tied to a hook rigidly mounted into a wall. A pulse of height 1.9 cm is sent down the rope. The tension in the rope is F = 29 N.
(B) What is the height of the pulse that returns?
To find the height of the pulse that returns, we need to consider the principles of wave reflection and the properties of the rope.
When the pulse reaches the rigidly mounted hook, it will be reflected back along the rope. However, the pulse will undergo a change in direction and its height will also change.
To determine the height of the returning pulse, we can use the principle of conservation of mechanical energy. The total mechanical energy of the pulse is given by the sum of its kinetic energy and potential energy.
At the highest point of the pulse's motion, it comes to rest momentarily, so its kinetic energy is zero. Thus, the total mechanical energy is equal to the potential energy at the highest point.
The potential energy of an object with mass m at a height h is given by the equation:
PE = mgh,
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
In this case, the mass of the pulse is negligible compared to the mass of the rope. So we can assume that the pulse's potential energy is solely determined by the height it reaches.
Let's set up the equation using the given values:
PE_initial = PE_final
mgh_initial = mgh_final
Since the mass of the pulse does not change and acceleration due to gravity is constant, we can cancel out those terms:
h_initial = h_final
This implies that the height of the returning pulse will be equal to the height of the initial pulse.
Therefore, the height of the pulse that returns is also 1.9 cm (0.019 m).