8. A car of mass 1200 kg with a velocity of 25 m/s coasts uphill, but only gets to a maximum height of 24 m before stopping. How much energy was lost to friction, drag, etc.?

a. 92,800 J

b. 132,400 J

c. 168,000 J

d. 304,800 J

9. Suppose instead the energy lost to drag forces in the previous problem (#8) was 150,000 J and the angle of the incline was 2 as it rose the same 24 m vertical height mentioned before. What was the drag force (in Newtons)?

a. 218 N

b. 279 N

c. 291 N

d. 8,333 N

10. Consider a potential energy function U(x) given by U(x) = A(x x₀)² where A is a constant in units of kg/s² and x₀ is a constant in units of m. What force field would be created by this potential field?

a. F(x) = 2A(x x₀)

b. F(x) = 2A(x x₀)

c. F(x) = 3A(x x₀)²

d. F(x) = 3A(x x₀)²

e. F(x) = 3A(x x₀)³

f. F(x) = 3A(x x₀)³

12. A car driving on a level surface at a maximum constant speed feels a drag force of 800 N and its engine is doing 130 horsepower of work (1 horsepower = 746 Watts.) What is the maximum constant speed of the car on a level surface, in meters per second? Assume engine efficiency is 40%.

a. 32.1 m/s

b. 35.9 m/s

c. 38.8 m/s

d. 48.5 m/s

e. 58.0 m/s

13. How much total energy (including wasted energy) would the engine of the car from the previous problem (#12) consume after travelling 1 km on a level surface? Again, assume engine efficiency is 40%.

a. 800 kJ.

b. 2000 kJ.

c. 2500 kJ.

d. 3000 kJ.

work not needed