Centripetal Force Lab Report

Centripetal Force - Fg and Fr/acceleration

Roller coasters are successful in thrilling passengers as various forces and energy changes are involved. In a vertical loop on a rollercoaster, the centripetal force (Fc) is the force directed towards the centre of the circle, which keeps the cart on a circular path. The equation for the centripetal force is Fc=mv2r where m and v is the mass and the velocity of the roller coaster respectively and r is the radius of the circle.

Without the centripetal force, the roller coaster would travel in a straight line at a tangent to the circle and off the tracks. This is explained by Newton’s first law of motion: an object at rest will remain stationary and an object in motion will move at a constant velocity, unless acted upon by an unbalanced force, in this context the unbalanced force is the Fc. In a vertical circular loop, the weight force due to gravity, Fw, at 9.81ms-2 downwards and the reaction force, Fr, upwards provide the centripetal force. The weight force always acts vertically downwards. The reaction force always acts perpendicular to the tracks (towards the centre of the circle) and is the force exerted up onto the riders from the roller coaster.

G-forces

In this case, we consider the centripetal acceleration. Centripetal acceleration, ac, is the “rate of change of tangential velocity” [16] and can be expressed as ac = v2r. The centripetal acceleration acts inwards to the circle centre in the same direction as the Fc because Newton’s second law of motion states that the force on an object is equal to its mass multiplied by its acceleration - F=ma and F∝ a. The direction of a roller coaster in a loop is also constantly changing, thereby there is a change in velocity, which is