Answer:
Step-by-step explanation:
To calculate the elastic potential energy stored in the flea's legs before the leap, we need to use the conservation of energy principle, which states that the total energy of a system is constant.
Initially, the flea was at rest on the dog's cranium, so it had zero kinetic energy. However, it had some elastic potential energy stored in its legs due to the compression of its leg muscles before the leap. This energy was converted into kinetic energy as the flea jumped.
At the highest point of the flea's trajectory, it had reached its maximum height, so it had zero kinetic energy. However, it had some gravitational potential energy due to its height above the dog's cranium. This energy was equal to the amount of elastic potential energy stored in its legs before the leap.
Using the conservation of energy principle, we can equate the elastic potential energy stored in the flea's legs to its gravitational potential energy at the highest point of its trajectory:
Elastic potential energy = Gravitational potential energy
1/2 kx^2 = mgh
where k is the spring constant of the flea's leg muscles, x is the distance the flea's legs were compressed before the leap, m is the mass of the flea, g is the acceleration due to gravity, and h is the maximum height of the flea's trajectory.
We need to express all the quantities in SI units:
m = 0.10 g = 0.0001 kg
v = 1.25 m/s
h = 5.00 cm = 0.05 m
g = 9.81 m/s^2
To determine k and x, we need to use the fact that the kinetic energy of the flea at the moment of the leap is equal to the elastic potential energy stored in its legs:
1/2 mv^2 = 1/2 kx^2
Solving for x:
x = sqrt(mv^2/k)
Substituting the known values:
x = sqrt(0.0001*1.25^2/k)
Now, we can substitute the values of m, x, and h into the equation for the elastic potential energy:
1/2 kx^2 = mgh
1/2 k (0.00011.25^2/k) = 0.00019.81*0.05
0.000078125 k = 0.00004905
k = 0.627 N/m
Finally, we can substitute the value of k and x into the equation for the elastic potential energy:
1/2 kx^2 = 1/20.627(0.0001*1.25^2/k)^2
Elastic potential energy = 0.0000156 J
Therefore, the elastic potential energy stored in the flea's legs before the leap was 0.0000156 J.