In class we learned about Kate, a bungee jumper with mass ? = 50.0 kg who jumps off a bridge ofheight ℎ = 25.0 m above a river. After she jumps, the bungee cord – which behaves as an ideal springwith spring constant ? = 28.5 N/m – stretches to a new equilibrium with length ?? = 20.0 m. a) What is the unstretched length of the bungee cord without Kate attached? After hanging out at this new equilibrium for a bit, Kate starts to get worried. She yells up to her friend Ken, who is frantically trying to figure out how to hoist her back up. After a couple of hours of this, Katestarts to get hungry. She begs Ken to throw her down a backpack full of provisions with mass ? = 15.0 kg. Ken complies, dropping the bag from the bridge with no initial velocity. Throughout this problem, youmay neglect all sources of friction or other non-conservative forces. b) Kate catches the bag when it gets to her. What are the momenta of Kate and the bag just before she catches it? What about just after?
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.
In class we learned about Kate, a bungee jumper with mass ? = 50.0 kg who jumps off a bridge of
height ℎ = 25.0 m above a river. After she jumps, the bungee cord – which behaves as an ideal spring
with spring constant ? = 28.5 N/m – stretches to a new equilibrium with length ?? = 20.0 m.
a) What is the unstretched length of the bungee cord without Kate attached?
After hanging out at this new equilibrium for a bit, Kate starts to get worried. She yells up to her friend Ken, who is frantically trying to figure out how to hoist her back up. After a couple of hours of this, Kate
starts to get hungry. She begs Ken to throw her down a backpack full of provisions with mass ? = 15.0 kg. Ken complies, dropping the bag from the bridge with no initial velocity. Throughout this problem, you
may neglect all sources of friction or other non-conservative forces.
b) Kate catches the bag when it gets to her. What are the momenta of Kate and the bag just before she catches it? What about just after?
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