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pimuni
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1. A ski lift carries skiers along a 600-meter slope inclined at 30 degrees. Each chair has a mass of 50 kg, and each rider has a mass of 70 kg. The skier gets off at the top of the hill, so the chairs are empty for the return trip. Under maximum load conditions six riders per minute arrive at the top. If 60% of the energy supplied by the motors goes into overcoming friction, what average power must the motor supply?
This is what I have so far, but I am not sure if it is right:
W = F*d*cos(theta)
Power = W/t
since it says 6 ppl per minute make it to the top, i will use 6 ppl times their weight to get the force required. 6*70*9.8 = 4116 N
since the change in height is 300 m (600*sin30(theta)), then W = 4116(300) = 1236060 J
it said 6 ppl in 1 minute, do that's 60 seconds
power = W / t, so 1236060 j / 60 seconds = 20601 watts
since this is only 40% of the energy, 100% will be 51502.5 watts
im not sure if I did this right or not, because i didn't account for the mass of the chairs, since half are going up and half r going down, so their work cancels.
2 .
(53 and 27 are angles)
_______________
\ 53....37/
...\.../
T1 \.../ T2
...\.../
...[x]
T1 = .15 m
T2 = .2 m
A ball weight 5 Newtons is suspended by two strings as shown. Suppose the ball swings as a pendulum perpendicular to the plane of the page, achieving a maximum speed of 0.6 meters per second during its motion. Determine the magnitude and direction of the net force on the ball as it swings through the lowest point in its path.
here i am a bit stuck. i know that the lowest point is where the maximum speed will be held at. But I am not sure if the different angles make the net force point somewhere else than south. The horizontal acceleration will be 0, and the vertical will be 9.8. What else could I infere?
This is what I have so far, but I am not sure if it is right:
W = F*d*cos(theta)
Power = W/t
since it says 6 ppl per minute make it to the top, i will use 6 ppl times their weight to get the force required. 6*70*9.8 = 4116 N
since the change in height is 300 m (600*sin30(theta)), then W = 4116(300) = 1236060 J
it said 6 ppl in 1 minute, do that's 60 seconds
power = W / t, so 1236060 j / 60 seconds = 20601 watts
since this is only 40% of the energy, 100% will be 51502.5 watts
im not sure if I did this right or not, because i didn't account for the mass of the chairs, since half are going up and half r going down, so their work cancels.
2 .
(53 and 27 are angles)
_______________
\ 53....37/
...\.../
T1 \.../ T2
...\.../
...[x]
T1 = .15 m
T2 = .2 m
A ball weight 5 Newtons is suspended by two strings as shown. Suppose the ball swings as a pendulum perpendicular to the plane of the page, achieving a maximum speed of 0.6 meters per second during its motion. Determine the magnitude and direction of the net force on the ball as it swings through the lowest point in its path.
here i am a bit stuck. i know that the lowest point is where the maximum speed will be held at. But I am not sure if the different angles make the net force point somewhere else than south. The horizontal acceleration will be 0, and the vertical will be 9.8. What else could I infere?
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