Chapter 16: Problem 8: The length of nylon rope from which a mountain climber is suspended has a force constant of 1.75 × 10⁴ N/m. a) What is the frequency, in Hz, at which he bounces, given his mass and the mass of his equipment is 86 kg? b) How much would this rope stretch, in centimeters, to break the climber's fall if he free-falls 1.4m before the rope starts to stretch? c) What is the frequency, in Hz, at which he bounces, given his mass and the mass of his equipment is 86 kg if the rope is twice as long? d) How much would this rope stretch, in centimeters, to break the climber's fall if he free-falls 1.4 m before the rope runs out of slack if the rope was twice the length?
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
Chapter 16: Problem 8: The length of nylon rope from which a mountain climber is suspended has a force constant of 1.75 × 10⁴ N/m.
a) What is the frequency, in Hz, at which he bounces, given his mass and the mass of his equipment is 86 kg?
b) How much would this rope stretch, in centimeters, to break the climber's fall if he free-falls 1.4m before the rope starts to stretch?
c) What is the frequency, in Hz, at which he bounces, given his mass and the mass of his equipment is 86 kg if the rope is twice as long?
d) How much would this rope stretch, in centimeters, to break the climber's fall if he free-falls 1.4 m before the rope runs out of slack if the rope was twice the length?
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