The roller coaster in the figure below starts with a velocity of 17 m/s. One of the riders is a small girl of mass 31 kg. Find her apparent weight when the roller coaster is at locations B and C. At these two locations, the track is circular, with the radii of curvature given in the figure. The heights at points A, B, and C are
hA = 10 m,
hB = 20 m, and
hC = 0.
Assume friction is negligible and ignore the kinetic energy of the wheels.
To find the small girl's apparent weight at locations B and C, we need to consider the forces acting on her at those points.
First, let's consider point B. At this point, the roller coaster is moving in a circular path with a radius of curvature of RB. The small girl is experiencing both her actual weight (mg) and the centrifugal force (Fc) due to the circular motion.
To find the apparent weight at point B, we need to subtract the centrifugal force from her actual weight.
The centrifugal force (Fc) can be calculated using the formula:
Fc = m * v^2 / R
where:
m = mass of the small girl = 31 kg
v = velocity of the roller coaster = 17 m/s
R = radius of curvature at point B = RB
To find Fc, we substitute the given values into the formula:
Fc = 31 kg * (17 m/s)^2 / RB
Next, we subtract the centrifugal force Fc from the actual weight mg to find the apparent weight at point B:
Apparent weight at B = mg - Fc
Similarly, we can find the apparent weight at point C. At this point, the roller coaster is at the bottom of the loop, so there is no centrifugal force. The small girl is only experiencing her actual weight, which is the same as her apparent weight at point C.
To summarize:
- Apparent weight at B = mg - Fc
- Apparent weight at C = mg
To find the specific values, you will need to provide the radius of curvature at point B (RB) from the figure.