It is a fact that when a flexible rope is wrapped around a rough cylinder, a small force of magnitude F 0 at one end can resist a large force of magnitude F at the other end. The size of F depends on the angle θ through which the rope is wrapped around the cylinder (see the accompanying figure). The figure shows the graph of F (in pounds) versus θ (in radians), where F is the magnitude of the force that can be resisted by a force with magnitude F 0 = 10 lb for a certain rope and cylinder. (a) Estimate the values of F and d F / d θ when the angle θ = 10 radians. (b) It can be shown that the force F satisfies the equation d F / d θ = μ F , where the constant μ is called the coefficient of friction. Use the results in part (a) to estimate the value of μ .
It is a fact that when a flexible rope is wrapped around a rough cylinder, a small force of magnitude F 0 at one end can resist a large force of magnitude F at the other end. The size of F depends on the angle θ through which the rope is wrapped around the cylinder (see the accompanying figure). The figure shows the graph of F (in pounds) versus θ (in radians), where F is the magnitude of the force that can be resisted by a force with magnitude F 0 = 10 lb for a certain rope and cylinder. (a) Estimate the values of F and d F / d θ when the angle θ = 10 radians. (b) It can be shown that the force F satisfies the equation d F / d θ = μ F , where the constant μ is called the coefficient of friction. Use the results in part (a) to estimate the value of μ .
It is a fact that when a flexible rope is wrapped around a rough cylinder, a small force of magnitude
F
0
at one end can resist a large force of magnitude
F
at the other end. The size of
F
depends on the angle
θ
through which the rope is wrapped around the cylinder (see the accompanying figure). The figure shows the graph of
F
(in pounds) versus
θ
(in radians), where
F
is the magnitude of the force that can be resisted by a force with magnitude
F
0
=
10
lb for a certain rope and cylinder.
(a) Estimate the values of
F
and
d
F
/
d
θ
when the angle
θ
=
10
radians.
(b) It can be shown that the force
F
satisfies the equation
d
F
/
d
θ
=
μ
F
, where the constant
μ
is called the coefficient of friction. Use the results in part (a) to estimate the value of
μ
.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY