Before we go through the questions, we need to calculate and determine some values first.
r = 11.5 m
<span>m = 280 kg </span>
<span>Centripetal force = m x v^2/r = 280 x (17.1^2/11.5) = 7119.55 N
</span>
1) What is the magnitude of the normal force on the care when it is at the bottom of the circle.
<span>Centripetal force + mg = 7119.55 + (280 x 9.8) = 9863.55 N </span>
<span>2) What is the magnitude of the normal force on the car when it is at the side of the circle. </span>
<span>Centripetal force = 7119.55 N </span>
<span>3) What is the magnitude of the normal force on the car when it is at the top of the circle. </span>
<span>Centripetal force - mg = 7119.55 - (280 x 9.8) = 4375.55 N </span>
<span>4) What is the minimum speed of the car so that it stays in contact with the track at the top of the loop. </span>
√<span>(gr) </span>
√<span>(9.8 x 11.5) = 10.62 m/s</span>
The average speed is 20.8 m/s
Explanation:
The average speed for the trip is given by:

where
d is the distance covered
t is the time elapsed
For the trip in this problem, we have:
d = 187 km = 187,000 m is the distance travelled
The initial time is 10:00 pm while the arriving time is 12:30 am: this means that the time elapsed is 2.5 hours. Converting into seconds,

Therefore, the average speed for the trip is

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Answer:
option (E) 1,000,000 J
Explanation:
Given:
Mass of the suspension cable, m = 1,000 kg
Distance, h = 100 m
Now,
from the work energy theorem
Work done by the gravity = Work done by brake
or
mgh = Work done by brake
where, g is the acceleration due to the gravity = 10 m/s²
or
Work done by brake = 1000 × 10 × 100
or
Work done by brake = 1,000,000 J
this work done is the release of heat in the brakes
Hence, the correct answer is option (E) 1,000,000 J