Question

As a logging truck rounds a bend in the road, some logs come loose and begin to roll without slipping down the mountainside. The mountain slopes upward at 48.0? above the horizontal, and we can model the logs as solid uniform cylinders of mass 575kg and diameter 1.20m .

A) Find the acceleration of the logs as they roll down the mountain.

B) What is the friction force on the rolling logs? Is it kinetic or static?

Please show step-by-step how to solve.. thank you!!

As a logging truck rounds a bend in the road, some logs come loose and begin to roll without slipping down the mountainside. The mountain slopes upward at 48.0? above the horizontal, and we can model the logs as solid uniform cylinders of mass 575kg and diameter 1.20m . A) Find the acceleration of the logs as they roll down the mountain. B) What is the friction force on the rolling logs? Is it kinetic or static? Please show step-by-step how to solve.. thank you!!

Answer 1

The forces acting on the log are:

1. The component of the weight acting downwards the slope

(- mg cos 48deg)

2. The Force from rotational motion (going downwards)

T = I x (alpha)
T = Fr
Fr = I x (alpha)

F = I x(alpha) /r

= (1/2 m r^2) (alpha)/r.......alpha = a / r
= (1/2 mr (a / r)
= (1/2)ma

3. Force of friction going upwards = +Ff

unbalanced force = ma

+Ff - mg(cos 48) - (1/2)ma = ma
Ff - (575)(9.8)(.669) - (.5)(575)(4.86) = (575)(4.86)
Ff - 3770.55 - 1397.25 = 2794.5
Ff = 2373.3 N

acceleration = 4.86 m/s^2