Physics 12 - Unit 4 Take Home Test Question (4 marks) You must show all your work Occupants inside a rollercoaster car are released from rest at point A and then enter the "loop-the-loop" portion of the ride. The radius of the loop is r meters, and point A is h meters above the ground. A Prove that if the rollercoaster car to remain in contact with the track at point B, then h > >r. Ignore the effects of friction. Hint: 1. Let m equal the mass of the cart and then use conservation of mechanical energy between points A and B to get an equation involving v2 2. Apply Newton's 2nd Law to the circular motion of the cart at point B to get another equation involving vz 3. Equate your two expressions for v2 to get a relationship between h and r. 1 . magh = mg(2r ) + = mut mycar ) + Imvz = mah 2 . VN 2ritzr = h