Tom, who has a mass of 80 kg, and Mary, who has a mass of 50 kg, jump off a 20-m tall building and land on a fire net. The net compresses and they bounce back at the same time. Which of the following is not true?
A. Mary will bounce higher than Tom.
B. Tom's change of momentum= 3,200 kg m/s.
C. Tom will experience a greater force upon impact than Mary.
D. The energy in this event is concerted from potential to kinetic to elastic to kinetic.
I would really appreciate the help. Thanks in advance
Consider the transfer of energy for this problem:
Both Tom and Mary begin with
Potential Energy (20 meters above the net). As they're falling, the potential energy is gradually transfered into
Kinetic Energy. Eventually, they hit the net (20 meters below). But it's not over yet. Now, that kinetic energy is gradually going into the stretching of the fire net. As the fire net gets more and more stretched, the
Elastic Potential Energy builds, while Kinetic Energy decreases (think of compressing a spring). Eventually the spring reaches maximum compression. All this built up energy in the net wants to be used up. So now,
everything reverses. This energy is once again converted to kinetic energy. Tom and Mary begin flying back upwards and eventually they reach the same height they did originally. As wierd as this seems, it's true because there's no non-conservative forces such as air resistance acting on them (atleast that's what I'm assuming here
🙂).
That rules out choice A automatically as false, because Mary and Tom bounce to the same height they fell from originally (which was the same in this case).
However, we can go through the other choices too just to be sure:
The initial momentum as Tom hits the net is:
P=mv (80kg)(v) where v = sqrt(2gh); v = 20m/s
P = (80kg)(20m/s)
P = 1600kgm/s
This is the initial momentum. The final momentum is just opposite of that in direction but
equal in magnitude. This is because momentum is a vector. In order to assign a direction, we'll call downward momentum positive and upward negative.
Therefore change in momentum is:
P = Pfinal - Pinitial
P = -1600kg/ms - 1600kgm/s
P = -3200kg/ms
B is true.
The only force acting on Tom and Mary is the Force of Gravity (Weight).
This is the force upon impact.
Because Tom has a larger mass than Mary, Tom weights more.
Therefore
C is also true.
And finally, for the reasons discussed initially (for choice A),
D is also true.
