If a 40 kg brick and a 400 kg brick each dropped from 1 m above a trampoline, find the lowest position of each brick. Assume the trampoline is a simple spring obeying Hooke's law with a k value of 12 000 N/m.
So, I used
mg(h+x)=1/2 k x^2
then solved for x in each case.
and got 2 different values out of the quadratic formula:
-0.223 m and -0.0000242 m
given the question, how can I rule one of the answers out and choose the reasonable answer?
6000x^2-40kx- 40*9.8*1=0 where k is 1, or 10
x= (+40k+-sqrt(1600k^2+9.4E6)/12,000
for k=1
x= (40+-3067)/12000= 25cm ignore the -x, it has no physical meaning, the trampoline will not deform upward.
for k=10
x= (+400+-sqrt(160000+9.4E6)/12000
x=(400+-3093)/12000=29cm
check my math.
you lost be. k= 12 000 N/m
where are you getting 1 or 10
To determine the lowest position of each brick dropped onto the trampoline, we need to choose the reasonable answer from the two obtained values (-0.223 m and -0.0000242 m) using physical reasoning.
First, let's analyze the situation. When the bricks drop onto the trampoline, they compress the trampoline springs and store potential energy in the springs. This potential energy is then converted into kinetic energy as the springs push the bricks back up. At the lowest position, all the initial potential energy is transformed into the maximum kinetic energy by the time the bricks reach the lowest point of the bounce.
Now, let's examine the negative answers we obtained from the quadratic equation:
-0.223 m: This negative value suggests that the brick has penetrated through the trampoline and is now below the trampoline's surface, which is not physically possible. So we can confidently rule out this value.
-0.0000242 m: This value represents a very small compression of the trampoline springs (less than a millimeter). It is possible for the springs to compress to this extent. Additionally, this value is close to zero, indicating that the brick is hovering slightly above the trampoline surface at the lowest point of the bounce.
Therefore, the reasonable answer for the lowest position of each brick is approximately -0.0000242 m, which suggests that the bricks are hovering just above the trampoline surface at the lowest point of the bounce.