Question

Derive an algebraic equation for the vertical force that the bench exerts on the book at the lowest point of the circular path in terms of the book’s mass mb, tangential speed vb, radius R of the path, and physical constants, as appropriate. Do not substitute any numerical values for variables or physical constants.

Answer 1

Answer:

The algebraic equation is:

$F_{v} =\frac{m_{b}v_{b}^{2} }{R} -m_{b} g$

Explanation:

Given information:

mb = book's mass

vb = tangential speed

R = radius of the path

Question: Derive an algebraic equation for the vertical force, Fv = ?

To derive the equation, we need to draw a force diagram for this case, please, see the attached diagram. As you can see, there are three types of forces acting on the system. Two up and one of the weight acting down. Therefore, the algebraic equation is as follows:

$F_{v} =\frac{m_{b}v_{b}^{2} }{R} -m_{b} g$

The variables were defined above and g is the gravity.