A roller coaster begins on a large hill. the motor that lifts the cars to the to

Question

A roller coaster begins on a large hill. the motor that lifts the cars to the top of the first hill operates at 15KW. The mass of the cars and its passengers is 2000kg. 1. If the motor can only run for 90 seconds, calculate the maximum height of the first hill. After the cars and passengers reach the top of the first hill, they descend down the other side of the hill and to the original starting elevation. On this descent, the cars and passengers lose 7,000 J of energy due to friction. 2. At this point, the track turns upward and launches the cars into the air at a 20 degree angle above the horizontal. Calculate the maximum height the cars and passengers travel to before returning to the ground. For obvious reasons, it is desirable to safely catch the passengers in a pit of marshmallows. The marshmallows behave as a spring that has a spring constant k = 20,000 N/m. 3. Determine how deep the pit of marshmallows must be to bring the cars and passengers to rest.

Explanation / Answer

1. 15KW=15000 J/sec --> within 90 seconds the motor can provide 15000*90 joules of energy = 1.35e6 J this power shall be transferred to the potential energy of the car --> mgh=1.35e6 --> h=68.87 meters 2. initial potential energy is 1.35e6 J if there was no friction all this energy was transferred to the kinetic energy. But 7000J was wasted of friction --> kinetic energy will be 1.343e6 J we may calculate the speed: mv^2/2=1.343e6 --> v=36.64 the angle is 20 degrees --> v_y=vsin20=12.53 m/sec and v_x=vcos20=34.43 m/sec to find the height use conservation of energy: mv_y^2/2 = mgh --> h=8 m 3. All energy of the car shall be transfred to the spring --> 1.343e6 = kx^2/2 --> x=11.6 m

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