Question

The world's fastest land animal (relative to its size) is Paratarsotomus macropalpis, a sesame seed-sized mite native to southern California. Scientists recently clocked P. macropalpis traveling 322 body lengths per second, which, to scale, would be like a person running 1,300 miles per hour. The time it takes for P. macropalpis to reach its top speed is only 31 milliseconds. Knowing this and knowing that P. macropalpis has a body length of 0.7 millimeters and a mass of 100 micrograms, calculate the force behind this mite in Newtons. N Round to the hundreth, Leave in scientific notation (ex. format 1.32 x 10-⁴).

Answer 1

To calculate the force exerted by a mite, find its acceleration by dividing its speed by the time taken to reach that speed. Then, apply Newton's second law by multiplying the mite's mass by its acceleration. The result, rounded to the hundredth and in scientific notation, is approximately 7.27 x 10^-5 Newtons.

Step-by-step explanation:

To calculate the force exerted by Paratarsotomus macropalpis, we first need to determine the acceleration of the mite as it reaches its top speed in 31 milliseconds (0.031 seconds). Since we know it travels 322 body lengths per second, and one body length is 0.7 millimeters, its speed (v) is:

v = 322 body lengths/sec × 0.7 mm/body length = 225.4 mm/sec

The acceleration (a) can be found using the formula:

a = v / t where t is the time taken to reach that speed, which is 0.031 seconds.

Thus:

a = (225.4 mm/sec) / (0.031 sec) = 7274.19 mm/s² or 7.27419 m/s² (converting mm to m).

To find the force (F), we use Newton's second law:

F = m × a

The mass (m) of the mite is given as 100 micrograms, which is 100 × 10⁻¶ kg = 1 × 10⁻· kg (converting micrograms to kilograms).

Finally:

F = (1 × 10⁻· kg) × (7.27419 m/s²) = 7.27419 × 10⁻· N or approximately 7.27 × 10⁻⁵ Newtons.