a) at a minimum, how many motors will you need? b) at a minimum, how long will h

Question

a) at a minimum, how many motors will you need?

b) at a minimum, how long will horizontal track need to be?

You just got a job with Six Flags designing the next roller coaster. The idea is use magnetic motors to accelerate the car across a long horizontal section and then sharply turn upward and travel vertically for 70 m. To save money on operating costs the cars are extremely aerodynamic and the track has very low friction. At maximum capacity, the car should have mass of 5,000 kg. The magnetic motors provide a constant 15 m/s^2 of acceleration, but each motor can only supply 10,000 J of energy before it risks burning out. a At a minimum, how many motors will you need? b) At a minimum, how long will horizontal track need to be?

Explanation / Answer

The car has mass 5000 kg to be lifted 70 m. Thus, the work needed for that is

W = m g h

--> W = 3.43E6 J

As each motor has 10,000 J to spare,

# of motors = 3.43E6 J / (10 000 J/motor)

= 343 motors   [ANSWER, PART A]

******************

As a = 15 m/s^2, and

W = m a d

--> d = w / [ m a ]

Thus,

d = 45.7 m   [ANSWER]

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