Answer:
854.39 N
Explanation:
The formula for the fundamental frequency of a stretched string is given as,
f = 1/2L√(T/m)..................... Equation 1
Where f = fundamental frequency, L = Length of the wire, T = Tension, m = mass per unit length.
Given: f = 261.6 Hz, L = 0.6 m, m = (5.2×10⁻³/0.6) = 8.67×10⁻³ kg/m.
Substitute into equation 1
261.6 = 1/0.6√(T/8.67×10⁻³)
Making T the subject of the equation,
T = (261.6×0.6×2)²(8.67×10⁻³)
T =854.39 N
Hence the tension of the wire is 854.39 N.
Answer:
Explanation:
The instantaneous velocity of a point mass that executes a simple harmonic movement is given by:
Where:
Express the amplitude in meters:
The angular frequency can be found using the next equation:
Using the data provided:
At the equilibrium position:
The answer is:
1.8 meters.
Explanation:
An athlete swinging can be considered a pendulum.
The pendulum's maximum height is the point at which it changes direction, which means that its velocity is equal to zero. In this point, for the mechanical energy conservation, all its kinetic energy is transformed into potential energy. Similarly, when the pendulum is at its resting position (when the athlete grabs the rope), its energy is totally kinetic.
Therefore we can say that:
Solving for h:
As we can see, the maximum height is independent on the mass and on the length of the rope, therefore it will be the same for the 100kg-athlete as it is for the 50kg-athlete, since their initial speeds are the same.
We know that the <span>50kg-athlete reached a height of 1.8 m, h</span>ence, the maximum height reached by the 100kg-athlete will be
1.8 m.