When a rattlesnake strikes, its head accelerates from rest to a speed of 30 m/s in 0.64 s seconds. Assume for simplicity that the only moving part of the snake is its head of mass 100 g. How much (average) power does the rat-
tlesnake need to accelerate its head that fast?
Answer in units of W
a = (30 - 0)m/s / 0.64s = 46.88m/s^2.
Fs = mg = 0.1kg * 9.8N/kg = 0.98N @ 0 deg = Force of snake.
d=0.5at^2=0.5 * 46.88 * (0.64)^2=9.60m.
P=F * d/t = 0.98 * (9.6/0.64) = 14.7W.
To find the average power required for the rattlesnake to accelerate its head, we need to use the formula for power:
Power (P) = Work (W) / Time (t)
To calculate the work done, we can use the formula:
Work (W) = Force (F) * Distance (d)
First, let's calculate the force applied by the rattlesnake's head. We can use Newton's second law of motion:
Force (F) = Mass (m) * Acceleration (a)
Given that the mass of the rattlesnake's head is 100 g = 0.1 kg, and the acceleration is the change in velocity divided by the time taken (assuming constant acceleration), we can calculate the acceleration:
Acceleration (a) = Change in velocity (Δv) / Time (t)
The change in velocity is given as 30 m/s, and the time is given as 0.64 s. Plugging these values into the equation:
Acceleration (a) = 30 m/s / 0.64 s
Now we can calculate the force:
Force (F) = 0.1 kg * (30 m/s / 0.64 s)
Next, we need to determine the distance over which the force is applied. Since the rattlesnake's head is accelerating from rest, we can assume this is the distance traveled during acceleration. The distance can be calculated using the equation for displacement with constant acceleration:
Distance (d) = (1/2) * Acceleration (a) * Time (t)^2
In this case, since the initial velocity is zero, the equation simplifies to:
Distance (d) = (1/2) * Acceleration (a) * Time (t)^2
Plugging in the values:
Distance (d) = (1/2) * 30 m/s * (0.64 s)^2
Now we have all the values needed to calculate the work:
Work (W) = Force (F) * Distance (d)
Finally, we can calculate the average power by dividing the work by the time:
Power (P) = Work (W) / Time (t)
Now, let's calculate the values and find the answer.