Question

A spider of mass m is swinging back and forth at the end of a strand of silk of length L. During the spider's swing the strand makes a maximum angle of θ with the vertical. What is the speed of the spider at the low point of its motion, when the strand of silk is vertical? Express your answer in terms of the variables m , θ, L, and g.

Answer 1

v =√[2g*L (1-cosθ)]

Step-by-step explanation:

To solve this question, we would be using the law of energy conservation equation. The law of energy conservation is mathematically written as

Ek1 + Ep1 = Ek2 + Ep2, where

Ek1 is the kinetic energy, which is also Zero

Ep1 is the potential energy which is represented by the formula, m*g*L*cosθ

Ek2 is also the kinetic energy, given as ½m*v^²

Ep2 is the potential energy with the formula, m*g*L

If we substitute the defined equations into the primary equation, we have

0 - m*g*L*cosθ = ½m*v^² - m*g*L

½mv² = m*g*L - m*g*L*cosθ

½mv² = m*g*L (1-cosθ)

v² = 2g*L (1-cosθ)

v =√[2g*L (1-cosθ)]