Companion to the reading passage Falling Sideways: The Hidden Physics of Turns, Loops, and Orbits. Answer each question, then click Check. Multiple-choice and number questions grade themselves; for written answers, compare yours with the model answer and checklist, then score yourself honestly.
A coffee cup slides across a car’s dashboard as the car rounds a tight exit ramp. Highway engineers design ramps so that friction between the tires and the road can turn a car safely. An engineer analyzed a 1,200-kg car rounding a flat, curved ramp with a radius of 50. m at a constant speed of 15 m/s.
1. Substitute numerical values into a mathematical representation that can be used to determine the magnitude of the centripetal force needed to keep this car on the curved ramp. Then calculate the force.
2. The same car rounds the same ramp at twice the speed. Which row correctly describes the centripetal force now needed and its direction?
(Centripetal force needed / Direction of centripetal force)
A stunt team tested a motorcycle on a vertical circular loop with a radius of 6.0 m. Sensors recorded the motorcycle’s speed at the very top of the loop, where the rider is upside down. The track can only push on the motorcycle; it cannot pull. The results are shown in Table 1.
Table 1: Speed at the Top of the Loop
| Trial | Speed at top of loop (m/s) |
|---|---|
| 1 | 6.0 |
| 2 | 7.5 |
| 3 | 9.0 |
Data are representative values for practice.
3. A team member makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
4. Free-body diagram of the motorcycle at the top of the loop in Trial 3; the center of the loop is below the dot (up is up). Assume the motorcycle and rider have a combined mass of 250 kg. Choose the direction of the gravitational force Fg and determine its magnitude (g = 9.81 N/kg).
5. Same motorcycle (250 kg, Trial 3, top of the loop). Choose the direction of the normal force FN exerted by the track and determine its magnitude.
The International Space Station orbits about 4.0 × 105 m above Earth’s surface at a speed of about 7.7 × 103 m/s. At that altitude, Earth’s gravitational field strength is about 8.7 N/kg, compared with 9.81 N/kg at Earth’s surface. Yet astronauts inside the station float freely and appear weightless.
6. Which statement best explains why the astronauts appear to float inside the ISS?
A cyclist rides around the same flat curve several times, each time at a different constant speed. Students calculated the centripetal force needed on the cyclist-and-bike system for each speed and noticed that the force did not increase by the same amount for each equal increase in speed.
7. Which graph best represents the relationship between the centripetal force needed and the cyclist’s speed for this curve?