The passengers in a roller coaster car feel 1.60 times heavier than their true weight as the car goes through a dip with a 24.0 m radius of curvature. What is the car's speed at the bottom of the dip?
Which equation do I use?
V= 2(pi)r/t = 2(pi)rtf = wr
.6 g = v^2 / r
To solve this problem, you can use the equation that relates the apparent weight of the passengers to the speed of the roller coaster at the bottom of the dip. The equation is:
Apparent Weight = True Weight + (Centripetal Force / Gravitational Force) x True Weight
In this case, the apparent weight of the passengers is 1.60 times their true weight. The centripetal force acting on the passengers is equal to the gravitational force acting on them at the bottom of the dip. So we can rewrite the equation as:
1.6 * True Weight = True Weight + (mv^2 / r) / True Weight
Simplifying this equation will allow us to solve for the speed of the roller coaster at the bottom of the dip.
Now, let's address the equations you mentioned:
1. V = 2πr / t: This equation relates the linear speed (V) of an object moving in a circular path to the radius (r) of the path and the time (t) taken to complete one full revolution. However, it is not applicable to this problem because we do not have information about the time taken for the roller coaster to complete one full revolution.
2. W = 2πr × t × f: This equation is used to calculate the work (W) done when a force (f) is applied along the displacement (2πr) in the direction of the force for a certain time (t). It does not apply to this problem because we do not have information about the work done.
3. w = wr: This equation is not relevant to this problem as it does not represent a physical relationship.
To summarize, use the equation that relates the apparent weight of the passengers to the speed of the roller coaster at the bottom of the dip to solve for the speed.