Unit 4 - Problem 2 ==> Rollercoaster with friction

Given

• Similar to Unit 4 - Problem 2
• Initial height = 45 meters
• There is a 20 meter section before the loop that creates a friction force.
• What is maximum value of friction force?

Rationale

• $$E_{potential} = E_{top-of-loop} + E_{kinetic-top-of-loop}$$
• $$m_{car} a_{gravity} h = (m_{car} a_{gravity} h_{top-of-loop}) + (\frac{1}{2} m_{car} V^2_{top-of-loop}) - (F_{x-friction-max}  d_{bad-track}) $$

Calculations

• $$(200*45*10) = (200*20*10) + (\frac{1}{2}*200*10^2) - (F_{x-friction-max}*20)$$
• $$90000 = 40000 + 10000 - (F_{x-friction-max}*20) $$
• $$90000 - 50000 = -20F_{x-friction-max}$$
• $$40000 =  -20F_{x-friction-max}$$
• $$F_{x-friction} = -2000 $$