Final answer:
A student's apparent weight at the bottom of a dip on a roller coaster is the sum of the gravitational force and the centripetal force required for circular motion. For a 55kg student traveling at 10m/s through a 15m radius dip, the apparent weight is approximately 905.67N.
Step-by-step explanation:
To calculate the student's apparent weight at the bottom of the dip on the roller coaster, we must consider the forces acting on the student. At the bottom of the dip, the student experiences both the force due to gravity (weight) and the centripetal force required to keep them moving in a circular path. The apparent weight is the sum of the normal force exerted by the roller coaster seat on the student and the gravitational force.
The formula for centripetal force (Fc) is Fc = (m * v2) / r, where m is mass, v is velocity, and r is the radius of the circular path.
For the student with a mass of 55kg, riding at a speed of 10m/s through a dip with a radius of 15m, the centripetal force is calculated as follows: Fc = (55kg * (10m/s)2) / 15m = (5500kg * m/s2) / 15m = 366.67N.
The gravitational force (Fg) is the product of the mass and acceleration due to gravity (g = 9.8m/s2), so Fg = 55kg * 9.8m/s2 = 539N. Finally, the apparent weight at the bottom of the dip is the sum of Fc and Fg which is 366.67N + 539N = 905.67N.
Therefore, the student's apparent weight at the bottom of the dip is approximately 905.67N.