Circular motion, gravitation, and work and energy

Please solve the following problems and show all work.

 

  1. A 5600 kg mass car is taking a turn at 72 m/s. If the frictional force here is 44,000N, what is the radius of curvature of the turn?
  2. Up where the ISS (International Space Station) orbits at 387 km, even though they are weightless there still is an acceleration due to gravity. Calculate its value and what it is in respect to 8g at the Earth’s surface.
  3. Going back to the previous question, how long does it take the ISS to orbit? (You must calculate this and not just look it up!)
  4. If a person on a 35.0 m diameter Ferris wheel feels 30% heavier at the bottom of the wheel, how fast is it going around?
  5. A large box with mass 45 kg is being pushed up a ramp at a 32o incline at a constant velocity by a man pushing parallel to the incline for 7.80 m. If the coefficient of kinetic friction is 0.25, what is:
    1. The force the man is pushing on the box.
    2. The work done by the man on the box.
    3. The force of friction.
    4. The work done by the friction force.
  6. A spring with negligible mass is suspended next to a ruler such that the end of the spring at equilibrium is at the 0 cm mark on the ruler. If a 3.0 kg mass is suspended from the spring and it stretches so that the end of the spring is at the 17 cm mark, what is the spring constant k?
  7. A softball having a mass of 0.45 kg is pitched horizontally at spring with spring constant 78 N/m. If the ball hits the spring and compresses it 56 cm, how fast was the softball moving initially?
  8. A roller coaster is a height of 120 m and has a series of dips. What is he velocity at the bottom (assuming this is 120 m below the top) and what is the velocity at a bump that is 75 m above the ground?

On this weeks homework assignment number 8, the problem makes much more sense if you assume it is at rest at the top of the track. Also, be sure to ignore friction. If we had to worry about friction, there would need to by much more information given in the question.

 

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