Kinesin is a "motor protein" responsible for moving materials within living cells. If it exerts a 6.0 -pN force, what acceleration will it give a molecular complex with mass \(3.0 \times 10^{-18} \mathrm{kg} ?\)

Kinesin is a fascinating type of motor protein that plays an integral role in the cellular world. It functions like a tiny molecular machine within living cells, moving biological material along structures called microtubules. Kinesin is vital for tasks such as transporting nutrients, organelles, and other cellular cargo from one part of a cell to another, and is also involved in cell division processes.

This protein has a mechanism that converts chemical energy, derived from the hydrolysis of ATP (adenosine triphosphate), into mechanical work. This energy conversion enables the movement, with the kinesin 'walking' along microtubules, attaching and detaching its 'feet' one at a time. Despite the tiny forces it operates with, typically in the range of picoNewtons, it has a significant impact on cellular functions. Understanding how kinesin works could help in fields like biomedical engineering, where the targeted delivery of drugs to specific cells is crucial.

In physics, being consistent with units is essential for accurate calculations. The International System of Units (SI) specifies the Newton (N) as the standard unit of force. In microscopic scales, like those involving motor proteins such as kinesin, forces are so small that they are measured in picoNewtons (pN).

To smoothly transition between these scales, conversion is required. One picoNewton equals one trillionth of a Newton (1 pN = 10^{-12} N). Hence, when a force of 6.0 pN is applied, it is equivalent to an incredibly small force of 6.0 x 10^{-12} N in SI units. It's important to convert picoNewtons to Newtons before calculating related physical quantities to ensure proper scale and to use Newton's laws, which are framed in SI units.

According to Newton's second law of motion, the force exerted on an object is equal to its mass times its acceleration (F = ma). To find the acceleration, we rearrange the law: (a = F/m). This demonstrates the direct relationship between force and acceleration, indicating that higher forces lead to greater accelerations, given the same mass.

When calculating acceleration, as in the case of kinesin moving a molecular complex, the mass and the force need to be in SI units, i.e., kilograms for mass and Newtons for force. Following the conversion of the given 6.0 pN force into Newtons, we can see how even an almost imperceptible force can result in a substantial acceleration when the mass of the object is extremely small, such as the 3.0 x 10^{-18} kg cellular cargo. The result is an astonishingly high acceleration, reflecting the highly sensitive and precise movements that occur at the cellular level.