The cable of the 1800 kg elevator cab snaps when the cab is at rest at the first floor, where the cab bottom is a distance d= 3.7 m above a spring of spring constant k = 0.15 MN/m. A safety device clamps the cab against guide rails so that a constant frictional force of 4.4 kN opposes the cab’s motion. (a) Find the speed of the cab just before it hits the spring. (b) Find the maximum distance x that the spring is compressed (the frictional force still acts during this compression). (c) Find the distance that the cab will bounce back up the shaft. (d) Using conservation of energy, find the approximate total distance that the cab will move before coming to rest. (Assume that the frictional force on the cab is negligible when the cab is stationary.)
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.
The cable of the 1800 kg elevator
cab snaps when the cab is at
rest at the first floor, where the cab bottom
is a distance d= 3.7 m above a spring of
spring constant k = 0.15 MN/m. A safety
device clamps the cab against guide rails so
that a constant frictional force of 4.4 kN
opposes the cab’s motion. (a) Find the
speed of the cab just before it hits the
spring. (b) Find the maximum distance x
that the spring is compressed (the frictional
force still acts during this compression).
(c) Find the distance that the cab
will bounce back up the shaft. (d) Using
conservation of energy, find the approximate
total distance that the cab will move before coming to rest.
(Assume that the frictional force on the cab is negligible when the
cab is stationary.)
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