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Chapter 5: Problem 36

In the process of mitosis (cell division), two motor proteins pull on a spindle pole, each with a 7.3 -pN force. The two force vectors make a \(65^{\circ}\) angle. What's the magnitude of the force the two motor proteins exert on the spindle pole?

Short Answer

Expert verified
After applying the values and calculating, the magnitude of the resultant force that the two motor proteins exert on the spindle pole is approximately 13.63 pN.

Step by step solution

01

Understand the Forces Involved and Translate them into Vectors

Two motor proteins exert equal forces of 7.3 pN on a spindle pole, making an angle of \(65^{\circ}\) with each other. We denote these forces as Force1 and Force2, each represented as a vector with magnitude 7.3 (in the direction each one is applied). This translates the problem into a vectors' analysis context.
02

Apply the Law of Cosines to Determine the Resultant Force

To find the resultant force (magnitude of the combined forces), we apply the law of cosines for the addition of two vectors. The formula is \(|F_{res}| = \sqrt{ |Force1|^2 + |Force2|^2 + 2|Force1||Force2| \cos \theta}\), where \(|Force1|\) and \(|Force2|\) are magnitudes of the forces, and \(\theta\) is the angle between them.
03

Calculate the magnitude of the Resultant Force

Substitute the given values into the formula. We have \(|Force1| = |Force2| = 7.3\,pN\), and \(\theta = 65^{\circ}\). It is crucial to remember to convert degrees into radians before making the calculation because trigonometric calculations in most programming or calculation tools are in radians. Thus, the entry becomes \(|F_{res}| = \sqrt{ 7.3^2 + 7.3^2 + 2*7.3*7.3 \cos 65^{\circ}}\)

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